Gaussian fluctuation for spatial average of super-Brownian motion

被引：3

作者：

Li, Zenghu ^{[1
]}

Pu, Fei ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2023年 / 41卷 / 04期

基金：

国家重点研发计划; 美国国家科学基金会;

关键词：

super-Brownian motion; stochastic heat equation; central limit theorem; CENTRAL-LIMIT-THEOREM; EQUATION;

D O I：

10.1080/07362994.2022.2079530

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let {u(t,x)}((t,x)is an element of R+xR) be the density of one-dimensional super-Brownian motion starting from Lebesgue measure. Using the Laplace functional of super-Brownian motion, we , prove that as N -> infinity the normalized spatial integral N-1/2 integral(xN)(0) [u(t ,z) - 1] dz converges jointly in (t, x) to Brownian sheet in distribution.

引用

页码：752 / 769

页数：18

共 25 条

[1]

Balan R.M., 2022, PREPRINT

[2]

Balan R.M., 2021, PREPRINT

[3] CONVERGENCE CRITERIA FOR MULTIPARAMETER STOCHASTIC PROCESSES AND SOME APPLICATIONS [J].

BICKEL, PJ ;

WICHURA, MJ .

ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (05) :1656-&

[4]

Chen L., 2014, STOCK PARTIAL DIFFER, V2, P316

[5] Central limit theorems for parabolic stochastic partial differential equations [J].

Chen, Le ;

Khoshnevisan, Davar ;

Nualart, David ;

Pu, Fei .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2022, 58 (02) :1052-1077

[6] Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method [J].

Chen, Le ;

Khoshnevisan, Davar ;

Nualart, David ;

Pu, Fei .

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2023, 11 (01) :122-176

[7] Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition [J].

Chen, Le ;

Khoshnevisan, Davar ;

Nualart, David ;

Pu, Fei .

JOURNAL OF FUNCTIONAL ANALYSIS, 2022, 282 (02)

[8]

Dawson D.A., 1993, Lecture Notes in Mathematics, V1541, P1

[9] A Central Limit Theorem for the stochastic wave equation with fractional noise [J].

Delgado-Vences, Francisco ;

Nualart, David ;

Zheng, Guangqu .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2020, 56 (04) :3020-3042

[10]

Etheridge A., 2000, An Introduction to Superprocesses

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