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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:
60H25Random operators and equations
34C27Almost and pseudo-almost periodic solutions of ODE
34F05ODE with randomness
34G20Nonlinear ODE in abstract spaces
60H10Stochastic ordinary differential equations