Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations

被引：39

作者：

Chang, Yong-Kui ^{[1
,2
]}

Zhao, Zhi-Han ^{[1
]}

N'Guerekata, G. M. ^{[3
]}

Ma, Ruyun ^{[2
]}

机构：

[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

[2] NW Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

[3] Morgan State Univ, Dept Math, Baltimore, MD 21251 USA

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 02期

基金：

中国博士后科学基金;

关键词：

Stepanov-like almost automorphy; Square-mean almost automorphy; Stochastic differential equations; ALMOST-PERIODIC SOLUTIONS; MILD SOLUTIONS; EXISTENCE;

D O I：

10.1016/j.nonrwa.2010.09.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a new concept of Stepanov-like almost automorphy (or S-2-almost automorphy) for stochastic processes. We use the results obtained to investigate the existence and uniqueness of a Stepanov-like almost automorphic mild solution to a class of nonlinear stochastic differential equations in a real separable Hilbert space. Our main results extend some known ones in the sense of square-mean almost automorphy. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1130 / 1139

页数：10

共 25 条

[1] Almost periodic solutions of neutral functional differential equations [J].

Abbas, S. ;

Bahuguna, D. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 55 (11) :2593-2601

[2]

[Anonymous], 1992, STOCH STOCH REP, DOI DOI 10.1080/17442509208833758

[3]

[Anonymous], VISNIK KIIV U MM

[4]

[Anonymous], P AM MATH S IN PRESS

[5]

Bezandry PH, 2008, ELECTRON J QUAL THEO, P1

[6] Existence of almost periodic solutions to some stochastic differential equations [J].

Bezandry, Paul H. ;

Diagana, Toka .

APPLICABLE ANALYSIS, 2007, 86 (07) :819-827

[7] Existence of almost periodic solutions to some functional integro-differential stochastic evolution equations [J].

Bezandry, Paul H. .

STATISTICS & PROBABILITY LETTERS, 2008, 78 (17) :2844-2849

[8] CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC + ALMOST PERIODIC FUNCTIONS [J].

BOCHNER, S .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1964, 52 (04) :907-&

[9] NEW APPROACH TO ALMOST PERIODICITY [J].

BOCHNER, S .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1962, 48 (12) :2039-&

[10] Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semi-linear differential equations in Hilbert spaces [J].

Chang, Yong-Kui ;

Zhao, Zhi-Han ;

Nieto, Juan J. .

REVISTA MATEMATICA COMPLUTENSE, 2011, 24 (02) :421-438

← 1 2 3 →