Almost sure functional central limit theorems for multiparameter stochastic processes

被引：0

作者：

Czerebak-Morozowicz, E. B. ^{[1
]}

Rychlik, Z. ^{[2
]}

Urbanek, M. ^{[2
]}

机构：

[1] Rzeszow Tech Univ, Dept Math, PL-35959 Rzeszow, Poland

[2] Marie Curie Sklodowska Univ, Inst Math, PL-20031 Lublin, Poland

来源：

CONDENSED MATTER PHYSICS | 2008年 / 11卷 / 02期

关键词：

almost sure central limit theorem; multiparameter stochastic process; Glivenko-Cantelli type theorem; logarithmic averages; WEAK-CONVERGENCE; LAW;

D O I：

暂无

中图分类号：

O469 [凝聚态物理学];

学科分类号：

070205 ;

摘要：

We present almost sure central limit theorems for stochastic processes whose time parameter ranges over the d-dimensional unit cube. Our purpose here is to generalize the classic functional central limit theorem of Prokhorov (1956) for such processes. We prove multidimensional analogues of Glivenko-Cantelli type theorems.

引用

页码：371 / 381

页数：11

共 50 条

[31] Almost Sure Central Limit Theorem for strictly stationary processes
Lesigne, E
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (06) : 1751 - 1759
[32] Refinement of the almost sure central limit theorem for associated processes
M. A. Vronskii
Mathematical Notes, 2000, 68 : 444 - 451
[33] On the almost-sure central limit theorem for point processes
Chebchoub, A
Manoubi, R
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (01): : 83 - 86
[34] Refinement of the almost sure central limit theorem for associated processes
Vronskii, MA
MATHEMATICAL NOTES, 2000, 68 (3-4) : 444 - 451
[35] On the random functional central limit theorems in L-2[0, 1] with almost sure convergence
Rychlik, Zdzislaw
Skublewski, Wojciech
Walczynski, Tomasz
ACTA SCIENTIARUM MATHEMATICARUM, 2007, 73 (3-4): : 745 - 765
[36] Almost sure limit theorems for stable distributions
Wu, Qunying
STATISTICS & PROBABILITY LETTERS, 2011, 81 (06) : 662 - 672
[37] Integral analogues of almost sure limit theorems
Chuprunov A.
Fazekas I.
Periodica Mathematica Hungarica, 2005, 50 (1-2) : 61 - 78
[38] On almost sure max-limit theorems
Fahrner, I.
Stadtmuller, U.
Statistics & Probability Letters, 37 (03):
[39] Classical and almost sure local limit theorems
Szewczak, Zbigniew
Weber, Michel
DISSERTATIONES MATHEMATICAE, 2023, 589 : 1 - 97
[40] Classical and almost sure local limit theorems
Szewczak, Zbigniew
Weber, Michel
DISSERTATIONES MATHEMATICAE, 2023, 589 : 1 - 97

← 1 2 3 4 5 →