Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability

Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability

Year:    2013

Author:    Guoli Zhou, Boling Guo, Zhenting Hou

Journal of Partial Differential Equations, Vol. 26 (2013), Iss. 3 : pp. 251–288

Abstract

The existence and uniqueness of mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis-Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild solution of a general stochastic evolution equation perturbed by Levy process. Then the authors prove the moment exponential stability, almost sure exponential stability and comparison principles of the mild solution. As applications, the stability and comparison principles of stochastic heat equation with Levy jump are given.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v26.n3.4

Journal of Partial Differential Equations, Vol. 26 (2013), Iss. 3 : pp. 251–288

Published online:    2013-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    38

Keywords:    Stochastic evolution equation

Author Details

Guoli Zhou

Boling Guo

Zhenting Hou