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

共 50 条

[11] Pathwise uniqueness for stochastic evolution equations with Hölder drift and stable Lévy noise
Desheng Yang
Nonlinear Differential Equations and Applications NoDEA, 2018, 25
[12] Random attractors of reaction-diffusion equations without uniqueness driven by nonlinear colored noise
Gu, Anhui
Wang, Bixiang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 486 (10)
[13] On existence and uniqueness of reflected solutions of stochastic equations driven by symmetric stable processes
Engelbert, HJ
Kurenok, VP
Zalinescu, A
FROM STOCHASTIC CALCULUS TO MATHEMATICAL FINANCE: THE SHIRYAEV FESTSCHRIFT, 2006, : 227 - 248
[14] Pathwise uniqueness for stochastic differential equations driven by pure jump processes
Zheng, Jiayu
Xiong, Jie
STATISTICS & PROBABILITY LETTERS, 2017, 130 : 100 - 104
[15] Uniqueness for solutions of Fokker-Planck equations related to singular SPDE driven by L,vy and cylindrical Wiener noise
Wiesinger, Sven
JOURNAL OF EVOLUTION EQUATIONS, 2013, 13 (02) : 369 - 394
[16] PATHWISE UNIQUENESS OF THE STOCHASTIC HEAT EQUATION WITH SPATIALLY INHOMOGENEOUS WHITE NOISE
Neuman, Eyal
ANNALS OF PROBABILITY, 2018, 46 (06) : 3090 - 3187
[17] Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane
Liang, ZX
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 83 (02) : 303 - 317
[18] Remark on pathwise uniqueness of stochastic differential equations driven by Levy processes
Takeuchi, Atsushi
Tsukada, Hiroshi
STOCHASTIC ANALYSIS AND APPLICATIONS, 2019, 37 (02) : 155 - 170
[19] On the existence and uniqueness of pairwise stable networks
Hellmann, Tim
INTERNATIONAL JOURNAL OF GAME THEORY, 2013, 42 (01) : 211 - 237
[20] On the existence and uniqueness of pairwise stable networks
Tim Hellmann
International Journal of Game Theory, 2013, 42 : 211 - 237

← 1 2 3 4 5 →