Squaremean almost automorphic solutions for some stochastic differential equations
Authors:
Miaomiao Fu and Zhenxin Liu
Journal:
Proc. Amer. Math. Soc. 138 (2010), 36893701
MSC (2010):
Primary 60H25, 34C27, 34F05, 34G20
Published electronically:
May 6, 2010
MathSciNet review:
2661567
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Additional Information
Abstract: The concept of squaremean almost automorphy for stochastic processes is introduced. The existence and uniqueness of squaremean almost automorphic solutions to some linear and nonlinear stochastic differential equations are established provided the coefficients satisfy some conditions. The asymptotic stability of the unique squaremean almost automorphic solution in the squaremean sense is discussed.
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 S. Bochner, Curvature and Betti numbers in real and complex vector bundles. Univ. e Politec. Torino. Rend. Sem. Mat. 15 (195556), 225253. MR 0084160 (18:819c)
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 G. Da Prato and C. Tudor, Periodic and almost periodic solutions for semilinear stochastic equations. Stochastic Anal. Appl. 13 (1995), 1333. MR 1313204 (96e:60112)
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 G. M. N'Guérékata, Almost automorphic and almost periodic functions in abstract spaces. Kluwer Academic/Plenum Publishers, New York, 2001. MR 1880351 (2003d:43001)
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 G. M. N'Guérékata, Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations. Semigroup Forum 69 (2004), 8086. MR 2063980 (2005b:34119)
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 B. Øksendal, Stochastic differential equations. An introduction with applications. Sixth edition. Universitext. SpringerVerlag, Berlin, 2003. MR 2001996 (2004e:60102)
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Additional Information
Miaomiao Fu
Affiliation:
College of Mathematics, Jilin University, Changchun 130012, People’s Republic of China – and – School of Mathematics, Changchun Normal College, Changchun 130032, People’s Republic of China
Email:
mmfucaathy@yahoo.com.cn
Zhenxin Liu
Affiliation:
College of Mathematics, Jilin University, Changchun 130012, People’s Republic of China
Email:
zxliu@jlu.edu.cn
DOI:
http://dx.doi.org/10.1090/S0002993910103773
Keywords:
Almost automorphy,
stochastic differential equations
Received by editor(s):
October 27, 2009
Received by editor(s) in revised form:
January 11, 2010
Published electronically:
May 6, 2010
Additional Notes:
The second author is partially supported by NSFC Grant 10801059, SRFDP Grant 20070183053, the 985 Program of Jilin University, and the science research fund at Jilin University.
Communicated by:
Yingfei Yi
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
