Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements
Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k...
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Gespeichert in:
| Autor*in: |
Parker, Robert [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematica sinica - Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985, 35(2019), 5 vom: 15. Apr., Seite 583-596 |
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| Übergeordnetes Werk: |
volume:35 ; year:2019 ; number:5 ; day:15 ; month:04 ; pages:583-596 |
| Links: |
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| DOI / URN: |
10.1007/s10114-019-8058-5 |
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| Katalog-ID: |
OLC2062524994 |
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| 520 | |a Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. | ||
| 650 | 4 | |a Real separable Banach space | |
| 650 | 4 | |a double array of independent random elements | |
| 650 | 4 | |a strong law of large numbers | |
| 650 | 4 | |a almost sure convergence | |
| 650 | 4 | |a Rademacher type | |
| 650 | 4 | |a Banach space | |
| 650 | 4 | |a convergence in | |
| 700 | 1 | |a Rosalsky, Andrew |4 aut | |
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10.1007/s10114-019-8058-5 doi (DE-627)OLC2062524994 (DE-He213)s10114-019-8058-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Parker, Robert verfasserin aut Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type Banach space convergence in Rosalsky, Andrew aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 35(2019), 5 vom: 15. Apr., Seite 583-596 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:35 year:2019 number:5 day:15 month:04 pages:583-596 https://doi.org/10.1007/s10114-019-8058-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 35 2019 5 15 04 583-596 |
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10.1007/s10114-019-8058-5 doi (DE-627)OLC2062524994 (DE-He213)s10114-019-8058-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Parker, Robert verfasserin aut Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type Banach space convergence in Rosalsky, Andrew aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 35(2019), 5 vom: 15. Apr., Seite 583-596 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:35 year:2019 number:5 day:15 month:04 pages:583-596 https://doi.org/10.1007/s10114-019-8058-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 35 2019 5 15 04 583-596 |
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10.1007/s10114-019-8058-5 doi (DE-627)OLC2062524994 (DE-He213)s10114-019-8058-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Parker, Robert verfasserin aut Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type Banach space convergence in Rosalsky, Andrew aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 35(2019), 5 vom: 15. Apr., Seite 583-596 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:35 year:2019 number:5 day:15 month:04 pages:583-596 https://doi.org/10.1007/s10114-019-8058-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 35 2019 5 15 04 583-596 |
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10.1007/s10114-019-8058-5 doi (DE-627)OLC2062524994 (DE-He213)s10114-019-8058-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Parker, Robert verfasserin aut Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type Banach space convergence in Rosalsky, Andrew aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 35(2019), 5 vom: 15. Apr., Seite 583-596 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:35 year:2019 number:5 day:15 month:04 pages:583-596 https://doi.org/10.1007/s10114-019-8058-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 35 2019 5 15 04 583-596 |
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10.1007/s10114-019-8058-5 doi (DE-627)OLC2062524994 (DE-He213)s10114-019-8058-5-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Parker, Robert verfasserin aut Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type Banach space convergence in Rosalsky, Andrew aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 35(2019), 5 vom: 15. Apr., Seite 583-596 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:35 year:2019 number:5 day:15 month:04 pages:583-596 https://doi.org/10.1007/s10114-019-8058-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 AR 35 2019 5 15 04 583-596 |
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Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements |
| abstract |
Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 |
| abstractGer |
Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 |
| abstract_unstemmed |
Abstract For a double array {Vm,n,m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p (1 ≤ p ≤ 2) Banach space and an increasing double array {bm,n,m ≥ 1, n ≥ 1} of positive constants, the limit law $$max_{1\leq{k}\leq{m},1\leq{l}\leq{n}}\parallel\Sigma_{i=1}^k\Sigma_{j=1}^l{V_{i,j}}\parallel/b_{m,n}\rightarrow0$$ a.c. and in ℒp as m ∨ n → ∞ is shown to hold if $$\Sigma_{m=1}^\infty\Sigma_{n=1}^\infty{E}\parallel{V_{m,n}}\parallel^p/{b_{m,n}^p}<\infty$$. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019 |
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GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2018 |
| container_issue |
5 |
| title_short |
Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements |
| url |
https://doi.org/10.1007/s10114-019-8058-5 |
| remote_bool |
false |
| author2 |
Rosalsky, Andrew |
| author2Str |
Rosalsky, Andrew |
| ppnlink |
129236772 |
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n |
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| hochschulschrift_bool |
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| doi_str |
10.1007/s10114-019-8058-5 |
| up_date |
2024-07-03T15:23:22.082Z |
| _version_ |
1803571903419383808 |
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7.402648 |