TY - JOUR
T1 - Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability
AU - Zhou , Guoli
AU - Guo , Boling
AU - Hou , Zhenting
JO - Journal of Partial Differential Equations
VL - 3
SP - 251
EP - 288
PY - 2013
DA - 2013/09
SN - 26
DO - http://doi.org/10.4208/jpde.v26.n3.4
UR - https://global-sci.org/intro/article_detail/jpde/5164.html
KW - Stochastic evolution  equation
KW - Levy processes
KW - mild solution
KW - stability
AB - <p>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.</p>