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

Kai Liu ()
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Kai Liu: Tianjin Normal University

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1625-1646

Abstract: 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.

Keywords: Stability sensitive to small delays; Pathwise exponential stability; Stochastic delay evolution equation; 60H15; 60G15; 60H05 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0750-8

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