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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space | Chang et al. Advances in Difference Equations 2011 2011 9 http www.advancesindifferenceequations.eom content 2011 1 9 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space Yong-Kui Chang 1 Zhi-Han Zhao1 and Gaston Mandata N Guérékata2 Correspondence lzchangyk@163. com department of Mathematics Lanzhou Jiaotong University Lanzhou Gansu 730070 PR China Full list of author information is available at the end of the article SpringerOpen0 Abstract This article deals primarily with the existence and uniqueness of square-mean almost automorphic mild solutions for a class of stochastic differential equations in a real separable Hilbert space. We study also some properties of square-mean almost automorphic functions including a compostion theorem. To establish our main results we use the Banach contraction mapping principle and the techniques of fractional powers of an operator. Mathematics Subject Classification 2000 34K14 60H10 35B15 34F05. Keywords Stochastic differential equations Square-mean almost automorphic processes Mild solutions 1 Introduction In this article we investigate the existence and uniqueness of square-mean almost automorphic solutions to the class of stochastic differential equations in the abstract form d x t - f t B1 x t Ax t g t B2x t dt h t B3x t dW t t e R 1.1 where A D A c L2 P H L2 P H is the infinitesimal generator of an analytic semigroup of linear operators T t t 0 on L2 P H Bi i 1 2 3 are bounded linear operators that can be viewed as control terms and W t is a two-sided standard onedimensional Brownian motion defined on the filtered probability space F P Ft where Ft Ơ W u W v u v t . Here f g and h are appropriate functions to be specified later. The concept of almost automorphy is an important generalization of the classical almost periodicity. They were introduced by Bochner 1 2 for more details about this .
