Stochastic functional differential equations with infinite delay: Existence and uniqueness of solutions, solution maps, Markov properties, and ergodicity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Wu, Fuke¹  Yin, George²  Mei, Hongwei³ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[3] Univ Cent Florida, Dept Math, Orlando, FL 32828 USA

关键词: Stochastic functional differential equation;    Infinite delay;    Solution map;    Adaptivity;    Markov property;    Invariant measure;   

DOI  :  10.1016/j.jde.2016.10.006

来源: Elsevier

【 摘 要 】

This work is devoted to stochastic functional differential equations (SFDEs) with infinite delay. First, existence and uniqueness of the solutions of such equations are examined. Because the solutions of the delay equations are not Markov, a viable alternative for studying further asymptotic properties is to use solution maps or segment processes. By examining solution maps, this work investigates the Markov properties as well as the strong Markov properties. Also obtained are adaptivity and continuity, mean-square boundedness, and convergence of solution maps from different initial data. This paper then examines the ergodicity of underlying processes and establishes existence of the invariant measure for SFDEs with infinite delay under suitable conditions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free