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Properties of stochastic integro-differential equations with infinite delay: Regularity, ergodicity, weak sense Fokker–Planck equations

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  • Mei, Hongwei
  • Yin, George
  • Wu, Fuke

Abstract

This work focuses on properties of stochastic integro-differential equations with infinite delay (or unbounded delay). Our main approach is to map the solution processes into another Polish space. Under suitable conditions, it is shown that the resulting processes are Markov. Furthermore, sufficient conditions for Feller properties, recurrence, ergodicity, and existence of invariant measures are obtained. Moreover, weak sense Fokker–Planck equations are derived for the underlying processes.

Suggested Citation

  • Mei, Hongwei & Yin, George & Wu, Fuke, 2016. "Properties of stochastic integro-differential equations with infinite delay: Regularity, ergodicity, weak sense Fokker–Planck equations," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3102-3123.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:3102-3123
    DOI: 10.1016/j.spa.2016.04.003
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    References listed on IDEAS

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    1. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
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    Cited by:

    1. Alipour, Sahar & Mirzaee, Farshid, 2020. "An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation," Applied Mathematics and Computation, Elsevier, vol. 371(C).

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