| Exis tence and st ability of μ-pseudo almost automorphic solutions for stochastic evolution equations |
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| 引用本文： | Jing CUI,Wenping RONG. Exis tence and st ability of μ-pseudo almost automorphic solutions for stochastic evolution equations[J]. Frontiers of Mathematics in China, 2019, 14(2): 261-280. DOI: 10.1007/s11464-019-0754-z |
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| 作者姓名： | Jing CUI Wenping RONG |
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| 作者单位： | College of Mathematics and Statistics |
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| 基金项目： | the Natural Science Foundation of Anhui Province (1708085MA03);the National Natural Science Foundation of China (Grant Nos. 11401010, 11571071). |
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| 摘 要： | We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.
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| 关 键 词： | STOCHASTIC evolution equation μ-pseudo ALMOST automorphic process fixed point THEOREM |
Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations |
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| Jing CUI,Wenping RONG. Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations[J]. Frontiers of Mathematics in China, 2019, 14(2): 261-280. DOI: 10.1007/s11464-019-0754-z |
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| Authors: | Jing CUI Wenping RONG |
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| Affiliation: | College of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China |
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| Abstract: | We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space. |
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| Keywords: | Stochastic evolution equation μ-pseudo almost automorphic process fixed point theorem |
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