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Uniform stability of autonomous linear stochastic functional differential equations in infinite dimensions

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  • Liu, Kai

Abstract

Existence, uniqueness and continuity of mild solutions are established for stochastic linear functional differential equations in an appropriate Hilbert space which is particularly suitable for stability analysis. An attempt is made to obtain some infinite dimensional stochastic extensions of the corresponding deterministic stability results. One of the most important results is to show that the uniformly asymptotic stability of the equations we try to handle is equivalent to their square integrability in some suitable sense. Subsequently, the stability results derived in retarded case are applied to coping with stability for a large class of neutral linear stochastic systems.

Suggested Citation

  • Liu, Kai, 2005. "Uniform stability of autonomous linear stochastic functional differential equations in infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1131-1165, July.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:7:p:1131-1165
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    Cited by:

    1. Boufoussi, Brahim & Hajji, Salah, 2010. "Successive approximation of neutral functional stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 324-332, March.
    2. Du, Bo, 2015. "Successive approximation of neutral functional stochastic differential equations with variable delays," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 609-615.

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