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

Ondrej Tybl, Bohdan Maslowski

Abstract: Existence of invariant measures and average stability in the mean are studied for stochas- tic differential equations driven by L ́evy process. In particular, some natural conditions are found that verify stabilization of the equation (in the sense of the existence of invari- ant measures) by jump noise terms. These conditions are verified in several examples.