Square-mean almost automorphic solutions for some stochastic differential equations

2010/01/18 by Miaomiao Fu, Fu, Miaomiao, Zhenxin Liu +1
Mathematics · #34C27 #34F05 #34G20 #60H25 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #math.DS #math.PR #msc:34C27 #msc:34F05 #msc:34G20 #msc:60H25

paper · pdf · doi:10.48550/arxiv.1001.3049

11 pages. Proc AMS, to appear

arxiv created 2010/01/18 · arxiv updated 2010/02/26

Abstract

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 square-mean sense is discussed.

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