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

作　　者：ZHOU Guoli GUO Boling HOU Zhenting 

机构地区：[1]College of Mathematics and Statistics, Chong Qing University, Chong Qing 401331,China. [2]Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China. [3]College of Mathematics and Statistics, Central South University, Changsha 410075, China.

出　　处：《Journal of Partial Differential Equations》2013年第3期251-288,共38页偏微分方程（英文版）

摘　　要：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.

关 键 词：Stochastic evolution equation Levy processes mild solution stability. 

分 类 号：O211[理学—概率论与数理统计]