Stochastic Functional Differential Equations With Infinite Delay: Existence And Uniqueness Of Solutions, Solution Maps, Markov Properties, And Ergodicity

Keywords

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

Abstract

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.

Publication Date

2-5-2017

Publication Title

Journal of Differential Equations

Volume

262

Issue

3

Number of Pages

1226-1252

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jde.2016.10.006

Socpus ID

85005896378 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85005896378

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