Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Dr.Yulan Lu, Institute of Computational Mathematics and Scientific/Engineering Computing, CAS
Inviter:
Title:
Ergodicity of backward Euler-Maruyama method for stochastic differential equations with piecewise continuous arguments
Time & Venue:
2018.11.21 16:00-17:00 Z311
Abstract:
Stochastic differential equations (SDEs) with piecewise continuous arguments (PCAs) arise in an attempt to extend the theory of functional differential equations (FDEs) with continuous arguments to differential equations with discontinuous arguments. These equations are widely applied in control theory and neural networks. In this talk, we consider the ergodicity of both SDEs with PCAs and the numerical solutions generated by the backward Euler-Maruyama (BEM) method. Since the solutions of SDEs with PCAs are not Markov, we consider the solutions of SDEs with PCAs at integer times, which are proved to be a Markov chain. Also obtained are the existence and uniqueness of the invariant measure for this Markov chain under suitable conditions, which means the ergodicity of this Markov chain. Moreover, the existence and uniqueness of the numerical invariant measure of the BEM method for SDEs with PCAs is obtained, which implies that the BEM preserves the ergodicity of the underlying Markov chain. Furthermore, it is revealed that the numerical invariant measure converges to the underlying invariant measure.