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

Abstract : This paper deals with the existence and uniqueness of (µ-pseudo) almost periodic mild solution to some evolution equations with Stepanov (µ-pseudo) almost periodic coefficients, in both determinist and stochastic cases. After revisiting some known concepts and properties of Stepanov (µ-pseudo) almost periodicity in complete metric space, we consider a semilinear stochastic evolution equation on a Hilbert separable space with Stepanov (µ-pseudo) almost periodic coefficients. We show existence and uniqueness of the mild solution which is (µ-pseudo) almost periodic in 2-distribution. We also generalize a result by Andres and Pennequin, according to which there is no purely Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients.
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Pré-publication, Document de travail
2017
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Soumis le : lundi 29 mai 2017 - 19:20:50
Dernière modification le : lundi 25 septembre 2017 - 09:48:25
Document(s) archivé(s) le : mercredi 6 septembre 2017 - 11:50:20

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  • HAL Id : hal-01478199, version 2
  • ARXIV : 1703.00282

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Fazia Bedouhene, Nouredine Challali, Omar Mellah, Paul Raynaud de Fitte, Mannal Smaali. Almost periodic solution in distribution for stochastic differential equations with Stepanov almost periodic coefficients. 2017. 〈hal-01478199v2〉

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