Sensitivity to Small Delays of Pathwise Stability for Stochastic Retarded Evolution Equations



Liu, Kai
(2018) Sensitivity to Small Delays of Pathwise Stability for Stochastic Retarded Evolution Equations. Journal of Theoretical Probability, 31 (3). pp. 1625-1646.

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Abstract

In this paper, we shall study the almost sure pathwise exponential stability property for a class of stochastic functional differential equations with delays, possibly, in the highest-order derivative terms driven by multiplicative noise. Instead of establishing a moment exponential stability as the first step and then proceeding to investigate the pathwise stability of the system under consideration, we shall develop a direct approach for this problem. As a consequence, we can show that some systems, which are not exponential momently stable, have the exponential stability not sensitive to small delays in the almost sure sense.

Item Type: Article
Uncontrolled Keywords: Stability sensitive to small delays, Pathwise exponential stability, Stochastic delay evolution equation
Depositing User: Symplectic Admin
Date Deposited: 07 Sep 2018 10:03
Last Modified: 19 Jan 2023 01:26
DOI: 10.1007/s10959-017-0750-8
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3025634