Global well-posedness of a class of stochastic equations with jumps

Guoli Zhou

doi:10.1186/1687-1847-2013-175

Abstract

The existence and uniqueness of a 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 jump processes. As applications, the regularity of a stochastic heat equation with jump is given. MSC: 76S05; 60H15

Highlights

In recent years, there have been many monographs concerning stochastic partial differential equations with Lévy jump and their applications in physics, economics, statistical mechanics, fluid dynamics and finance etc
There are a lot of works dealing with existence and uniqueness for stochastic partial differential equations with jump processes
In [ ], the existence and uniqueness for solutions of stochastic reaction diffusion equations driven by Poisson random measures are obtained

Summary

Introduction

There have been many monographs concerning stochastic partial differential equations with Lévy jump and their applications in physics, economics, statistical mechanics, fluid dynamics and finance etc. The existence, uniqueness, regularity for the mild solution of stochastic partial differential equations with Lévy jump are studied. There are a lot of works dealing with existence and uniqueness for stochastic partial differential equations with jump processes.

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Results

Conclusion