The almost sure local central limit theorem for products of partial sums under negative association

Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Jiang, Yuanying [verfasserIn] Wu, Qunying [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Negative association Products of partial sums Almost sure local central limit theorem Almost sure global central limit theorem

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2018(2018), 1 vom: 10. Okt.
Übergeordnetes Werk:	volume:2018 ; year:2018 ; number:1 ; day:10 ; month:10

Links:	Volltext

DOI / URN:	10.1186/s13660-018-1875-8

Katalog-ID:	SPR032602049

Internformat


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245	1	4	\|a The almost sure local central limit theorem for products of partial sums under negative association
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520			\|a Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.
650		4	\|a Negative association \|7 (dpeaa)DE-He213
650		4	\|a Products of partial sums \|7 (dpeaa)DE-He213
650		4	\|a Almost sure local central limit theorem \|7 (dpeaa)DE-He213
650		4	\|a Almost sure global central limit theorem \|7 (dpeaa)DE-He213
700	1		\|a Wu, Qunying \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of inequalities and applications \|d Heidelberg : Springer, 2005 \|g 2018(2018), 1 vom: 10. Okt. \|w (DE-627)320977056 \|w (DE-600)2028512-7 \|x 1029-242X \|7 nnns
773	1	8	\|g volume:2018 \|g year:2018 \|g number:1 \|g day:10 \|g month:10
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912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_95
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4700
936	b	k	\|a 31.49 \|q ASE
951			\|a AR
952			\|d 2018 \|j 2018 \|e 1 \|b 10 \|c 10

Indexfelder

author_variant	y j yj q w qw
matchkey_str	article:1029242X:2018----::hamssrlcletalmthoefrrdcsfatasmu
hierarchy_sort_str	2018
bklnumber	31.49
publishDate	2018
allfields	10.1186/s13660-018-1875-8 doi (DE-627)SPR032602049 (SPR)s13660-018-1875-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Jiang, Yuanying verfasserin aut The almost sure local central limit theorem for products of partial sums under negative association 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$. Negative association (dpeaa)DE-He213 Products of partial sums (dpeaa)DE-He213 Almost sure local central limit theorem (dpeaa)DE-He213 Almost sure global central limit theorem (dpeaa)DE-He213 Wu, Qunying verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 10. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:10 month:10 https://dx.doi.org/10.1186/s13660-018-1875-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 10 10
spelling	10.1186/s13660-018-1875-8 doi (DE-627)SPR032602049 (SPR)s13660-018-1875-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Jiang, Yuanying verfasserin aut The almost sure local central limit theorem for products of partial sums under negative association 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$. Negative association (dpeaa)DE-He213 Products of partial sums (dpeaa)DE-He213 Almost sure local central limit theorem (dpeaa)DE-He213 Almost sure global central limit theorem (dpeaa)DE-He213 Wu, Qunying verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 10. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:10 month:10 https://dx.doi.org/10.1186/s13660-018-1875-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 10 10
allfields_unstemmed	10.1186/s13660-018-1875-8 doi (DE-627)SPR032602049 (SPR)s13660-018-1875-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Jiang, Yuanying verfasserin aut The almost sure local central limit theorem for products of partial sums under negative association 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$. Negative association (dpeaa)DE-He213 Products of partial sums (dpeaa)DE-He213 Almost sure local central limit theorem (dpeaa)DE-He213 Almost sure global central limit theorem (dpeaa)DE-He213 Wu, Qunying verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 10. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:10 month:10 https://dx.doi.org/10.1186/s13660-018-1875-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 10 10
allfieldsGer	10.1186/s13660-018-1875-8 doi (DE-627)SPR032602049 (SPR)s13660-018-1875-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Jiang, Yuanying verfasserin aut The almost sure local central limit theorem for products of partial sums under negative association 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$. Negative association (dpeaa)DE-He213 Products of partial sums (dpeaa)DE-He213 Almost sure local central limit theorem (dpeaa)DE-He213 Almost sure global central limit theorem (dpeaa)DE-He213 Wu, Qunying verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 10. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:10 month:10 https://dx.doi.org/10.1186/s13660-018-1875-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 10 10
allfieldsSound	10.1186/s13660-018-1875-8 doi (DE-627)SPR032602049 (SPR)s13660-018-1875-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.49 bkl Jiang, Yuanying verfasserin aut The almost sure local central limit theorem for products of partial sums under negative association 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$. Negative association (dpeaa)DE-He213 Products of partial sums (dpeaa)DE-He213 Almost sure local central limit theorem (dpeaa)DE-He213 Almost sure global central limit theorem (dpeaa)DE-He213 Wu, Qunying verfasserin aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2018(2018), 1 vom: 10. Okt. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2018 year:2018 number:1 day:10 month:10 https://dx.doi.org/10.1186/s13660-018-1875-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.49 ASE AR 2018 2018 1 10 10
language	English
source	Enthalten in Journal of inequalities and applications 2018(2018), 1 vom: 10. Okt. volume:2018 year:2018 number:1 day:10 month:10
sourceStr	Enthalten in Journal of inequalities and applications 2018(2018), 1 vom: 10. Okt. volume:2018 year:2018 number:1 day:10 month:10
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Negative association Products of partial sums Almost sure local central limit theorem Almost sure global central limit theorem
dewey-raw	510
isfreeaccess_bool	true
container_title	Journal of inequalities and applications
authorswithroles_txt_mv	Jiang, Yuanying @@aut@@ Wu, Qunying @@aut@@
publishDateDaySort_date	2018-10-10T00:00:00Z
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Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Negative association</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Products of partial sums</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Almost sure local central limit theorem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Almost sure global central limit theorem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wu, Qunying</subfield><subfield code="e">verfasserin</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 inequalities and applications</subfield><subfield code="d">Heidelberg : Springer, 2005</subfield><subfield code="g">2018(2018), 1 vom: 10. 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author	Jiang, Yuanying
spellingShingle	Jiang, Yuanying ddc 510 bkl 31.49 misc Negative association misc Products of partial sums misc Almost sure local central limit theorem misc Almost sure global central limit theorem The almost sure local central limit theorem for products of partial sums under negative association
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topic_title	510 ASE 31.49 bkl The almost sure local central limit theorem for products of partial sums under negative association Negative association (dpeaa)DE-He213 Products of partial sums (dpeaa)DE-He213 Almost sure local central limit theorem (dpeaa)DE-He213 Almost sure global central limit theorem (dpeaa)DE-He213
topic	ddc 510 bkl 31.49 misc Negative association misc Products of partial sums misc Almost sure local central limit theorem misc Almost sure global central limit theorem
topic_unstemmed	ddc 510 bkl 31.49 misc Negative association misc Products of partial sums misc Almost sure local central limit theorem misc Almost sure global central limit theorem
topic_browse	ddc 510 bkl 31.49 misc Negative association misc Products of partial sums misc Almost sure local central limit theorem misc Almost sure global central limit theorem
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title	The almost sure local central limit theorem for products of partial sums under negative association
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title_full	The almost sure local central limit theorem for products of partial sums under negative association
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journal	Journal of inequalities and applications
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author_browse	Jiang, Yuanying Wu, Qunying
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title_sort	almost sure local central limit theorem for products of partial sums under negative association
title_auth	The almost sure local central limit theorem for products of partial sums under negative association
abstract	Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.
abstractGer	Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.
abstract_unstemmed	Abstract Let $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with $\mathrm{E}X_{1}=\mu>0$ and $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.
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title_short	The almost sure local central limit theorem for products of partial sums under negative association
url	https://dx.doi.org/10.1186/s13660-018-1875-8
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doi_str	10.1186/s13660-018-1875-8
up_date	2024-07-03T13:46:28.614Z
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Denote $S_{n}=\sum_{i=1}^{n}X_{i}, p_{k}=\mathrm{P}(a_{k}\leq ({\prod}_{j=1}^{k}S_{j}/(k!\mu^{k}) )^{1/(\gamma\sigma_{1} \sqrt{k})}< b_{k})$ and $\gamma=\sigma/\mu$ the coefficient of variation. Under some suitable conditions, we derive the almost sure local central limit theorem limn→∞1logn∑k=1n1kpkI{ak≤(∏j=1kSjk!μk)1/(γσ1k)<bk}=1a.s.,%$\lim_{n\rightarrow\infty}\frac{1}{\log n}\sum_{k=1}^{n} \frac{1}{kp_{k}}\mathrm{I} \biggl\{ a_{k}\leq \biggl(\frac {\prod_{j=1}^{k}S_{j}}{k!\mu^{k}} \biggr)^{1/(\gamma\sigma_{1} \sqrt {k})}< b_{k} \biggr\} =1 \quad\mbox{a.s.,} %$ where $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Negative association</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Products of partial sums</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Almost sure local central limit theorem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Almost sure global central limit theorem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wu, Qunying</subfield><subfield code="e">verfasserin</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 inequalities and applications</subfield><subfield code="d">Heidelberg : Springer, 2005</subfield><subfield code="g">2018(2018), 1 vom: 10. 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The almost sure local central limit theorem for products of partial sums under negative association

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