Existence of almost automorphic mild solutions to non-autonomous neutral stochastic differential equations

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• 作者：P. Revathi ; R. Sakthivel ; Yong Ren ; S. Marshal Anthoni
• 关键词：Non-autonomous stochastic neutral equations ; Stochastic processes ; Square mean automorphic solutions ; Evolution systems
• 刊名：Applied Mathematics and Computation
• 出版年：1 March, 2014
• 年：2014
• 卷：230
• 期：Complete
• 页码：639-649
• 全文大小：403 K

文摘

In this paper, we consider the existence and uniqueness of square-mean and weighted pseudo almost automorphic mild solutions to a class of nonautonomous stochastic neutral differential equations with infinite delay in real separable Hilbert spaces. A new set of sufficient conditions are established for obtaining the required result. To prove the main result, we use Banach contraction principle together with evolution family of operators. Some known results are generalized and improved. An application to the stochastic nonlinear heat equation with infinite delay is provided to illustrate the obtained theory.