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Existence and exponential stability of almost pseudo automorphic solution for neutral stochastic evolution equations driven by G-Brownian motion

Duan Pengju (School of Mathematics and Statistics, Suzhou University, Anhui, China), pjduan1981@hotmail.com

This paper mainly concerns the quasi sure exponential stability of square mean almost pseudo automorphic mild solution for a class of neutral stochastic evolution equations driven by G-Brownian motion. By means of evolution operator theorem and fixed point theorem, existence and uniqueness of square mean almost pseudo automorphic mild solution is obtained. Also, a series of sufficient conditions on exponential stability and quasi sure exponential stability are established.

Keywords: mild solution, almost pseudo automorphic, G-Brownian motion, quasi sure exponential stability, neutral stochastic evolution equation