Almost periodic solution in distribution for stochastic differential\n equations with Stepanov almost periodic coefficients

2017/03/01 by Fazia Bedouhene, Bedouhene, Fazia, Nouredine Challali +7
Mathematics · Engineering · #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.1703.00282

Abstract

This paper deals with the existence and uniqueness of (\μ-pseudo) almost\nperiodic mild solution to some evolution equations with Stepanov (\μ-pseudo)\nalmost periodic coefficients, in both determinist and stochastic cases. After\nrevisiting some known concepts and properties of Stepanov (\μ-pseudo) almost\nperiodicity in complete metric space, we consider a semilinear stochastic\nevolution equation on a Hilbert separable space with Stepanov (\μ-pseudo)\nalmost periodic coefficients. We show existence and uniqueness of the mild\nsolution which is (\μ-pseudo) almost periodic in 2-distribution. We also\ngeneralize a result by Andres and Pennequin, according to which there is no\npurely Stepanov almost periodic solutions to differential equations with\nStepanov almost periodic coefficients.\n

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