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Zbl 1202.60109
Fu, Miaomiao; Liu, Zhenxin
Square-mean almost automorphic solutions for some stochastic differential equations. (English)
[J] Proc. Am. Math. Soc. 138, No. 10, 3689-3701 (2010). ISSN 0002-9939; ISSN 1088-6826/e

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 2000:: *60H25 Random operators, etc.
34C27 Almost periodic solutions of ODE
34F05 ODE with randomness
34G20 Nonlinear ODE in abstract spaces
60H10 Stochastic ordinary differential equations

Keywords: almost automorphy

Cited in: Zbl 1211.60025

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