Approximation of Random Periodic Solutions for Neutral Type SDEs with Non-uniform Dissipativity

Abstract

The aim of this work is to approximate the random periodic solutions of neutral type stochastic differential equations (SDEs) with non-uniform dissipativity via the discretization method. The non-uniform dissipativity here means the drift satisfying dissipativity on average rather than uniform dissipativity concerning the time variables. On one hand, we show the existence and uniqueness of random periodic solutions for neutral type SDEs via the synchronous coupling approach when the starting time tends to −∞. On the other hand, using the Euler–Maruyama scheme on an infinite time horizon we study the existence and uniqueness of the numerical approximation of random periodic solution. During this procedure, the difficulties, which arose from the time-discretization of both the neutral term and the functional solutions, have to be dealt with.

Keywords

Random periodic solution / non-uniform dissipativity / neutral type stochastic differential equations / Euler–Maruyama method / 60H10 / 60H35 / 65C20 / 37H99

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Peking University