Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices
Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, C...
Ausführliche Beschreibung
Autor*in: |
Li, Deli [verfasserIn] |
---|
Format: |
Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
1998 |
---|
Anmerkung: |
© Plenum Publishing Corporation 1998 |
---|
Übergeordnetes Werk: |
Enthalten in: Journal of theoretical probability - Kluwer Academic Publishers-Plenum Publishers, 1988, 11(1998), 2 vom: Apr., Seite 443-459 |
---|---|
Übergeordnetes Werk: |
volume:11 ; year:1998 ; number:2 ; month:04 ; pages:443-459 |
Links: |
---|
DOI / URN: |
10.1023/A:1022687923455 |
---|
Katalog-ID: |
OLC2053621354 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | OLC2053621354 | ||
003 | DE-627 | ||
005 | 20230503160934.0 | ||
007 | tu | ||
008 | 200819s1998 xx ||||| 00| ||eng c | ||
024 | 7 | |a 10.1023/A:1022687923455 |2 doi | |
035 | |a (DE-627)OLC2053621354 | ||
035 | |a (DE-He213)A:1022687923455-p | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
082 | 0 | 4 | |a 510 |q VZ |
084 | |a 17,1 |2 ssgn | ||
100 | 1 | |a Li, Deli |e verfasserin |4 aut | |
245 | 1 | 0 | |a Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
264 | 1 | |c 1998 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
338 | |a Band |b nc |2 rdacarrier | ||
500 | |a © Plenum Publishing Corporation 1998 | ||
520 | |a Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. | ||
700 | 1 | |a Tomkins, R. J. |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Journal of theoretical probability |d Kluwer Academic Publishers-Plenum Publishers, 1988 |g 11(1998), 2 vom: Apr., Seite 443-459 |w (DE-627)129930903 |w (DE-600)357043-5 |w (DE-576)018191886 |x 0894-9840 |7 nnns |
773 | 1 | 8 | |g volume:11 |g year:1998 |g number:2 |g month:04 |g pages:443-459 |
856 | 4 | 1 | |u https://doi.org/10.1023/A:1022687923455 |z lizenzpflichtig |3 Volltext |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_OLC | ||
912 | |a SSG-OLC-MAT | ||
912 | |a SSG-OPC-MAT | ||
912 | |a GBV_ILN_24 | ||
912 | |a GBV_ILN_40 | ||
912 | |a GBV_ILN_70 | ||
912 | |a GBV_ILN_105 | ||
912 | |a GBV_ILN_2002 | ||
912 | |a GBV_ILN_2004 | ||
912 | |a GBV_ILN_2006 | ||
912 | |a GBV_ILN_2088 | ||
912 | |a GBV_ILN_4305 | ||
912 | |a GBV_ILN_4307 | ||
912 | |a GBV_ILN_4310 | ||
912 | |a GBV_ILN_4315 | ||
912 | |a GBV_ILN_4325 | ||
951 | |a AR | ||
952 | |d 11 |j 1998 |e 2 |c 04 |h 443-459 |
author_variant |
d l dl r j t rj rjt |
---|---|
matchkey_str |
article:08949840:1998----::opclwotetrtdoaihfrvlernovralsi |
hierarchy_sort_str |
1998 |
publishDate |
1998 |
allfields |
10.1023/A:1022687923455 doi (DE-627)OLC2053621354 (DE-He213)A:1022687923455-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Li, Deli verfasserin aut Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1998 Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. Tomkins, R. J. aut Enthalten in Journal of theoretical probability Kluwer Academic Publishers-Plenum Publishers, 1988 11(1998), 2 vom: Apr., Seite 443-459 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:11 year:1998 number:2 month:04 pages:443-459 https://doi.org/10.1023/A:1022687923455 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4325 AR 11 1998 2 04 443-459 |
spelling |
10.1023/A:1022687923455 doi (DE-627)OLC2053621354 (DE-He213)A:1022687923455-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Li, Deli verfasserin aut Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1998 Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. Tomkins, R. J. aut Enthalten in Journal of theoretical probability Kluwer Academic Publishers-Plenum Publishers, 1988 11(1998), 2 vom: Apr., Seite 443-459 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:11 year:1998 number:2 month:04 pages:443-459 https://doi.org/10.1023/A:1022687923455 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4325 AR 11 1998 2 04 443-459 |
allfields_unstemmed |
10.1023/A:1022687923455 doi (DE-627)OLC2053621354 (DE-He213)A:1022687923455-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Li, Deli verfasserin aut Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1998 Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. Tomkins, R. J. aut Enthalten in Journal of theoretical probability Kluwer Academic Publishers-Plenum Publishers, 1988 11(1998), 2 vom: Apr., Seite 443-459 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:11 year:1998 number:2 month:04 pages:443-459 https://doi.org/10.1023/A:1022687923455 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4325 AR 11 1998 2 04 443-459 |
allfieldsGer |
10.1023/A:1022687923455 doi (DE-627)OLC2053621354 (DE-He213)A:1022687923455-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Li, Deli verfasserin aut Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1998 Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. Tomkins, R. J. aut Enthalten in Journal of theoretical probability Kluwer Academic Publishers-Plenum Publishers, 1988 11(1998), 2 vom: Apr., Seite 443-459 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:11 year:1998 number:2 month:04 pages:443-459 https://doi.org/10.1023/A:1022687923455 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4325 AR 11 1998 2 04 443-459 |
allfieldsSound |
10.1023/A:1022687923455 doi (DE-627)OLC2053621354 (DE-He213)A:1022687923455-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Li, Deli verfasserin aut Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices 1998 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1998 Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. Tomkins, R. J. aut Enthalten in Journal of theoretical probability Kluwer Academic Publishers-Plenum Publishers, 1988 11(1998), 2 vom: Apr., Seite 443-459 (DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 0894-9840 nnns volume:11 year:1998 number:2 month:04 pages:443-459 https://doi.org/10.1023/A:1022687923455 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4325 AR 11 1998 2 04 443-459 |
language |
English |
source |
Enthalten in Journal of theoretical probability 11(1998), 2 vom: Apr., Seite 443-459 volume:11 year:1998 number:2 month:04 pages:443-459 |
sourceStr |
Enthalten in Journal of theoretical probability 11(1998), 2 vom: Apr., Seite 443-459 volume:11 year:1998 number:2 month:04 pages:443-459 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
dewey-raw |
510 |
isfreeaccess_bool |
false |
container_title |
Journal of theoretical probability |
authorswithroles_txt_mv |
Li, Deli @@aut@@ Tomkins, R. J. @@aut@@ |
publishDateDaySort_date |
1998-04-01T00:00:00Z |
hierarchy_top_id |
129930903 |
dewey-sort |
3510 |
id |
OLC2053621354 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2053621354</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503160934.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s1998 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1023/A:1022687923455</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2053621354</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)A:1022687923455-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Li, Deli</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1998</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Plenum Publishing Corporation 1998</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tomkins, R. J.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of theoretical probability</subfield><subfield code="d">Kluwer Academic Publishers-Plenum Publishers, 1988</subfield><subfield code="g">11(1998), 2 vom: Apr., Seite 443-459</subfield><subfield code="w">(DE-627)129930903</subfield><subfield code="w">(DE-600)357043-5</subfield><subfield code="w">(DE-576)018191886</subfield><subfield code="x">0894-9840</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:11</subfield><subfield code="g">year:1998</subfield><subfield code="g">number:2</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:443-459</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1023/A:1022687923455</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4310</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4315</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">11</subfield><subfield code="j">1998</subfield><subfield code="e">2</subfield><subfield code="c">04</subfield><subfield code="h">443-459</subfield></datafield></record></collection>
|
author |
Li, Deli |
spellingShingle |
Li, Deli ddc 510 ssgn 17,1 Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
authorStr |
Li, Deli |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)129930903 |
format |
Article |
dewey-ones |
510 - Mathematics |
delete_txt_mv |
keep |
author_role |
aut aut |
collection |
OLC |
remote_str |
false |
illustrated |
Not Illustrated |
issn |
0894-9840 |
topic_title |
510 VZ 17,1 ssgn Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
topic |
ddc 510 ssgn 17,1 |
topic_unstemmed |
ddc 510 ssgn 17,1 |
topic_browse |
ddc 510 ssgn 17,1 |
format_facet |
Aufsätze Gedruckte Aufsätze |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
nc |
hierarchy_parent_title |
Journal of theoretical probability |
hierarchy_parent_id |
129930903 |
dewey-tens |
510 - Mathematics |
hierarchy_top_title |
Journal of theoretical probability |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)129930903 (DE-600)357043-5 (DE-576)018191886 |
title |
Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
ctrlnum |
(DE-627)OLC2053621354 (DE-He213)A:1022687923455-p |
title_full |
Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
author_sort |
Li, Deli |
journal |
Journal of theoretical probability |
journalStr |
Journal of theoretical probability |
lang_code |
eng |
isOA_bool |
false |
dewey-hundreds |
500 - Science |
recordtype |
marc |
publishDateSort |
1998 |
contenttype_str_mv |
txt |
container_start_page |
443 |
author_browse |
Li, Deli Tomkins, R. J. |
container_volume |
11 |
class |
510 VZ 17,1 ssgn |
format_se |
Aufsätze |
author-letter |
Li, Deli |
doi_str_mv |
10.1023/A:1022687923455 |
dewey-full |
510 |
title_sort |
compact laws of the iterated logarithm for b-valued random variables with two-dimensional indices |
title_auth |
Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
abstract |
Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. © Plenum Publishing Corporation 1998 |
abstractGer |
Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. © Plenum Publishing Corporation 1998 |
abstract_unstemmed |
Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0. © Plenum Publishing Corporation 1998 |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2088 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4315 GBV_ILN_4325 |
container_issue |
2 |
title_short |
Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices |
url |
https://doi.org/10.1023/A:1022687923455 |
remote_bool |
false |
author2 |
Tomkins, R. J. |
author2Str |
Tomkins, R. J. |
ppnlink |
129930903 |
mediatype_str_mv |
n |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1023/A:1022687923455 |
up_date |
2024-07-03T19:54:38.407Z |
_version_ |
1803588970384195584 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2053621354</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503160934.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s1998 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1023/A:1022687923455</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2053621354</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)A:1022687923455-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Li, Deli</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1998</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Plenum Publishing Corporation 1998</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let $$({\text{B,||}} \cdot {\text{||}})$$ be a real separable Banach space and {X, Xn, m; (n, m) ∈ N2} B-valued i.i.d. random variables. Set $$S(n,m) = \sum\nolimits_{i = 1}^n {\sum\nolimits_{j = 1}^m {X_{i,j} ,(n,m) \in N} } ^2$$. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N2 is studied. There is a gap between the moment conditions for CLIL(N1) and those for CLIL(N2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence $${{\{ S(n,m)} \mathord{\left/ {\vphantom {{\{ S(n,m)} {\sqrt {2nm\log \log (nm);} (n,m) \in }}} \right. \kern-\nulldelimiterspace} {\sqrt {2nm\log \log (nm);} (n,m) \in }}N^r ({\alpha , }\varphi {)\} }$$ to be almost surely conditionally compact in B, where, for α ≥ 0, 1 ≤ r ≤ 2, Nr(α, φ) = {(n, m) ∈ N2; nα ≤ m ≤ nα exp{(log n)r−1 φ(n)}} and φ(·) is any positive, continuous, nondecreasing function such that φ(t)/(log log t)γ is eventually decreasing as t → ∞, for some γ > 0.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tomkins, R. J.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of theoretical probability</subfield><subfield code="d">Kluwer Academic Publishers-Plenum Publishers, 1988</subfield><subfield code="g">11(1998), 2 vom: Apr., Seite 443-459</subfield><subfield code="w">(DE-627)129930903</subfield><subfield code="w">(DE-600)357043-5</subfield><subfield code="w">(DE-576)018191886</subfield><subfield code="x">0894-9840</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:11</subfield><subfield code="g">year:1998</subfield><subfield code="g">number:2</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:443-459</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1023/A:1022687923455</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2002</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4310</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4315</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">11</subfield><subfield code="j">1998</subfield><subfield code="e">2</subfield><subfield code="c">04</subfield><subfield code="h">443-459</subfield></datafield></record></collection>
|
score |
7.4003086 |