P-DISTRIBUTION ALMOST PERIODIC SOLUTIONS OF SEMI-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH G-BROWNIAN MOTION*

摘要

As a class of recurrence, almost periodicity has been studied in stochastic differential equations (SDEs) under the framework of linear expectation. However, in the framework of nonlinear expectation, there are few literatures on Poisson stable solutions for SDEs and (pseudo) almost periodic solutions for SDEs with exponential dichotomy. This paper is devoted to the existence and asymptotical stability of p-distribution Poisson stable solutions for nonhomogeneous linear and semi-linear SDEs driven by G-Brownian motion satisfying exponential stability. Moreover, some existence results of (pseudo) almost periodic solution in p-distribution are established for semilinear SDEs driven by G-Brownian motion satisfying exponential dichotomy. Meanwhile, some examples are given to validate the obtained theoretical results.

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