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A note on almost sure exponential stability for stochastic partial functional differential equations

✍ Scribed by Kai Liu; Aubrey Truman

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
91 KB
Volume
50
Category
Article
ISSN
0167-7152

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✦ Synopsis

In a recent paper, Taniguchi (Stochastic Anal. Appl. 16 (5) (1998) 965 -975) investigated the almost sure exponential stability of the mild solutions of a class of stochastic partial functional di erential equations. Precisely, as small delay interval assumption is imposed, su cient conditions are obtained there to ensure the almost sure exponential stability of the mild solutions of the given stochastic systems. Unfortunately, the main results derived by him are somewhat restrictive to be applied for practical purposes. In the note we shall prove that for a class of stochastic functional di erential equations the small delay interval assumption imposed there is actually unnecessary and can be removed.

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