Moment asymptotics for super-Brownian motions

被引：0

作者：

Hu, Yaozhong ^{[1
]}

Wang, Xiong ^{[2
]}

Xia, Panqiu ^{[3
]}

Zheng, Jiayu ^{[4
]}

机构：

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[3] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[4] Shenzhen MSU BIT Univ, Fac Computat Math & Cybernet, Shenzhen 518172, Guangdong, Peoples R China

来源：

BERNOULLI | 2024年 / 30卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Intermittency; moment asymptotics; moment formula; super-Brownian motion; tail probability; two-sided moment bounds; STOCHASTIC HEAT-EQUATION; INTERMITTENCY;

D O I：

10.3150/23-BEJ1708

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, long-time and high-order moment asymptotics for super-Brownian motions (sBm's) are studied. By using a moment formula for sBm's (e.g. (Ann. Appl. Probab. 33 (2023) 3872-3915, Theorem 3.1)), precise upper and lower bounds for all positive integer moments at any time t > 0 of sBm's for certain initial conditions are achieved. Then, the moment asymptotics as time goes to infinity or as the moment order goes to infinity follow immediately. Additionally, as an application of the two-sided moment bounds, the tail probability estimates of sBm's are obtained.

引用

页码：3119 / 3136

页数：18

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