Averaging principle on infinite intervals for stochastic ordinary differential equations with Lévy noise

Abstract

In this paper, we establish an averaging principle on the infinite time intervals for semilinear stochastic ordinary differential equations with Lévy noise. In particular, under suitable conditions we prove that if the coefficients are Poisson stable (including periodic, quasi-periodic, almost periodic, almost automorphic etc), then there exists a unique L2-bounded solution of the original equation, which inherits the recurrence property of the coefficients, and the recurrent solution uniformly converges to the stationary solution of the averaged equation on the whole real axis in distribution sense.

Keywords

• averaging principle
• stochastic differential equations
• lévy noise
• periodic solution
• quasi-periodic solution
• almost periodic solution
• poisson stable solution