Almost sure central limit theorems for stochastic wave equations

被引：2

作者：

Li, Jingyu ^{[1
]}

Zhang, Yong ^{[1
]}

机构：

[1] Jilin Univ, Changchun, Peoples R China

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2023年 / 28卷

基金：

中国国家自然科学基金;

关键词：

almost sure central limit theorem; stochastic wave equation; Malliavin calculus; Poincar?-type inequality; UNIVERSAL RESULT; PARTIAL-SUMS; PRODUCTS;

D O I：

10.1214/23-ECP517

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we study almost sure central limit theorems for the spatial average of the solution to the stochastic wave equation in dimension d <= 2 over a Euclidean ball, as the radius of the ball diverges to infinity.This equation is driven by a general Gaussian multiplicative noise, which is temporally white and colored in space including the cases of the spatial covariance given by a fractional noise, a Riesz kernel, and an integrable function that satisfies Dalang's condition.

引用

页数：1

共 50 条

[21] Almost sure version of limit theorems
Ibragimov, IA
DOKLADY AKADEMII NAUK, 1996, 350 (03) : 301 - 303
[22] Central limit theorems for stochastic wave equations in dimensions one and two
Nualart, David
Zheng, Guangqu
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2022, 10 (02): : 392 - 418
[23] Central limit theorems for nonlinear stochastic wave equations in dimension three
Ebina, Masahisa
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2024, 12 (02): : 1141 - 1200
[24] Central limit theorems for stochastic wave equations in dimensions one and two
David Nualart
Guangqu Zheng
Stochastics and Partial Differential Equations: Analysis and Computations, 2022, 10 : 392 - 418
[25] Central limit theorems for nonlinear stochastic wave equations in dimension three
Masahisa Ebina
Stochastics and Partial Differential Equations: Analysis and Computations, 2024, 12 : 1141 - 1200
[26] An almost sure central limit theorem for stochastic approximation algorithms
Pelletier, M
JOURNAL OF MULTIVARIATE ANALYSIS, 1999, 71 (01) : 76 - 93
[27] An almost sure version of the central limit theorem for stochastic algorithms
Pelletier, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (02): : 235 - 238
[28] ON THE RANDOM FUNCTIONAL CENTRAL LIMIT THEOREMS WITH ALMOST SURE CONVERGENCE FOR SUBSEQUENCES
Rychlik, Zdzislaw
Szuster, Konrad
DEMONSTRATIO MATHEMATICA, 2012, 45 (02) : 283 - 296
[29] An almost sure central limit theorem for the stochastic heat equation
Li, Jingyu
Zhang, Yong
STATISTICS & PROBABILITY LETTERS, 2021, 177
[30] Almost sure functional central limit theorems for weakly dependent sequences
Chen, Shouquan
Lin, Zhengyan
STATISTICS & PROBABILITY LETTERS, 2008, 78 (13) : 1683 - 1693

← 1 2 3 4 5 →