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Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 261–280 | Cite as

Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations

  • Jing CuiEmail author
  • Wenping Rong
Research Article
  • 5 Downloads

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.

Keywords

Stochastic evolution equation μ-pseudo almost automorphic process fixed point theorem 

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Notes

Acknowledgements

This work was supported by the Natural Science Foundation of Anhui Province (1708085MA03) and the National Natural Science Foundation of China (Grant Nos. 11401010, 11571071).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsAnhui Normal UniversityWuhuChina

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