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