A note on existence of global solutions and invariant measures for jump SDEs with locally one-sided Lipschitz drift

摘要

We extend some methods developed by Albeverio, Brze′zniak andWu and we show how to apply them in order to prove existence of globalstrong solutions of stochastic differential equations with jumps, under a local one-sided Lipschitz condition on the drift (also known as a monotonicitycondition) and a local Lipschitz condition on the diffusion and jump coefficients, while an additional global one-sided linear growth assumption issatisfied. Then we use these methods to prove existence of invariant measures for a broad class of such equations.