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Exponential dichotomy of stochastic differential equations. (English) Zbl 1013.34048

Summary: Here, the author introduces a concept of exponential dichotomy for a stochastic evolution equation. Necessary and sufficient conditions for the exponential dichotomy are given. The obtained results are generalizations of the well-known results of R. Datko [SIAM J. Math. Anal. 3, 428-445 (1972)] and A. Ichikawa [Nonlinear Anal., Theory Methods Appl. 8, 805-815 (1984; Zbl 0547.47041)] on the stability of a class of stochastic equations.

MSC:

34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
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