Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise

被引：10

作者：

Xiong, Jie ^{[1
]}

Yang, Xu ^{[2
]}

机构：

[1] Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China

[2] North Minzu Univ, Sch Math & Informat Sci, Yinchuan, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2019年 / 129卷 / 08期

关键词：

Stochastic partial differential equation; Colored noise; Stable; Existence; Pathwise uniqueness; PARTIAL-DIFFERENTIAL EQUATIONS; STOCHASTIC-EQUATIONS; SUPERPROCESSES;

D O I：

10.1016/j.spa.2018.08.003

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 a stochastic partial differential equation (SPDE) with Holder continuous coefficient driven by an alpha-stable colored noise. The pathwise uniqueness is proved by using a backward doubly stochastic differential equation backward (SDE) to take care of the Laplacian. The existence of solution is shown by considering the weak limit of a sequence of SDE system which is obtained by replacing the Laplacian operator in the SPDE by its discrete version. We also study an SDE system driven by Poisson random measures. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：2681 / 2722

页数：42

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