一类带跳的随机微分方程解的Harnack不等式

Harnack Inequality for the Solution of a Class of Stochastic Differential Equations with Jumps

针对一类带泊松跳的随机微分方程,在一些合理的条件假设下研究了该类方程解的半群11():[()]x t t tP f x E f X I≤的Harnack不等式和Log-Harnack不等式问题.首先建立了两类半群之间的关系,同时使用耦合方法,结合Girsanov定理、H?lder不等式、Young不等式以及Ito公式,先后获得了Harnack和Log-Harnack的2种不等式.

In this paper, we study a class of stochastic differential equations with Poission jumps. Under some reasonable conditions, we deal with the issue of the Harnack inequalities and the Log-Harnack inequalities for the semigroup Pt^1f（x）：E[f（Xt^x）Iτ1≤t] of the solutions of such equations. We establish the relationship between the two kinds of semigroup. We also obtain two inequalities such as Hamack and Log-Hamack using the coupling argument, along with Girsanov theorem, Holder inequality, Young inequality and Ito formula.