Almost automorphy and various extensions for stochastic processes

被引：38

作者：

Bedouhene, Fazia ^{[1
]}

Challali, Nouredine ^{[1
]}

Mellah, Omar ^{[1
]}

de Fitte, Paul Raynaud ^{[2
]}

Smaali, Mannal ^{[1
]}

机构：

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

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 429卷 / 02期

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; ALMOST-PERIODIC-SOLUTIONS; ABSTRACT DIFFERENTIAL-EQUATIONS; WEIGHTED PSEUDO; STEPANOV-LIKE; COEFFICIENTS; EXISTENCE;

D O I：

10.1016/j.jmaa.2015.04.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1113 / 1152

页数：40

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