Abstract
The argument of Razumikhin-type has been well developed and showed significant advantage for the stability of stochastic functional differential equations in finite dimensions. However, so far there have been almost no results of Razumikhin-type on the stability of mild solutions of stochastic functional differential equations in infinite dimensions. The main aim of this paper is to establish Razumikhin-type stability theorems for stochastic functional differential equations in infinite dimensions. By virtue of these new criteria, we can establish the exponential stability of stochastic delay differential equations and stochastic delay partial differential equations.
This work was supported by EPSRC Grant No. GR/R37227.
Partially supported by Foundation for University Key Teacher by Ministry of Education of China, National Natural Science Foundation of China grant 10201018 and Doctor Promotional Foundation of Shandong grant 02BS127.
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Liu, K., Shi, Y. (2006). Razumikhin-Type Theorems of Infinite Dimensional Stochastic Functional Differential Equations. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) Systems, Control, Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 202. Springer, Boston, MA . https://doi.org/10.1007/0-387-33882-9_22
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DOI: https://doi.org/10.1007/0-387-33882-9_22
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