Almost automorphy and various extensions for stochastic processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:429

Article

Bedouhene, Fazia¹  Challali, Nouredine¹  Mellah, Omar¹  de Fitte, Paul Raynaud²  Smaali, Mannal¹ 

[1] Mouloud Mammeri Univ Tizi Ouzou, Lab Math Pures & Appl, Tizi Ouzou, Algeria

[2] Normandie Univ, Lab Raphael Salem, UMR CNRS 6085, Rouen, France

关键词: Weighted pseudo almost automorphic;    Square-mean almost automorphic;    Pseudo almost automorphic in quadratic mean;    Pseudo almost automorphic in distribution;    Ornstein-Uhlenbeck;    Semilinear stochastic differential equation;   

DOI  :  10.1016/j.jmaa.2015.04.014

来源: Elsevier

【 摘 要 】

We compare different modes of pseudo almost automorphy and variants for stochastic processes: in probability, in quadratic mean, or in distribution in various senses. We show by a counterexample that square-mean (pseudo) almost automorphy is a property which is too strong for stochastic differential equations (SDEs). Finally, we consider two semilinear SDEs, one with almost automorphic coefficients and the second one with pseudo almost automorphic coefficients, and we prove the existence and uniqueness of a mild solution which is almost automorphic in distribution in the first case, and pseudo almost automorphic in distribution in the second case. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free