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Square-mean almost automorphic solutions for some stochastic differential equations. (English) Zbl 1202.60109
Summary: The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established provided the coefficients satisfy some conditions. The asymptotic stability of the unique square-mean almost automorphic solution in the square-mean sense is discussed.

MSC:
60H25 Random operators and equations (aspects of stochastic analysis)
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
34G20 Nonlinear differential equations in abstract spaces
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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