Existence and uniqueness theorems for periodic Markov process and applications to stochastic functional differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:466

Article

Hu, Hongxiao¹  Xu, Liguang² 

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[2] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China

关键词: Periodic Markov process;    Stochastic functional differential equation;    Global attractive;    Infinite delay;   

DOI  :  10.1016/j.jmaa.2018.06.025

来源: Elsevier

【 摘 要 】

This work is devoted to an M-valued Markov process with a periodic transition probability function, where M is a Polish space. Sufficient conditions for the existence and uniqueness of the periodic Markov process are given. These existence theorems are rather general and the corresponding results in [1,11,15,23] are improved and generalized. The uniqueness theorems for the periodic Markov process are original. As applications, we study the existence, uniqueness and global attractivity of periodic solution for the periodic stochastic n-species Lotka-Voltrra competitive model with bounded delays and the periodic stochastic neural networks with infinite delay, respectively. Numerical simulations are presented to illustrate the main results. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free