Invariant measures and boundedness in the mean for stochastic equations driven by Levy noise

Abstract

Existence of invariant measures and average stability in the mean are studied for stochastic differential equations driven by Levy process. In particular, some natural conditions are found that verify stabilization of the equation (in the sense of the existence of invariant measures) by jump noise terms.

These conditions are verified in several examples.

Keywords

• Levy processes
• stochastic differential equations
• invariant measures
• stability