<i>P</i>-DISTRIBUTION ALMOST PERIODIC SOLUTIONS OF SEMI-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH <i>G</i>-BROWNIAN MOTION

Qigui Yang; Huoxia Liu; Xiaofang Lin

doi:10.11948/20210392

2022 Volume 12 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(6): 2230-2267

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Qigui Yang, Huoxia Liu, Xiaofang Lin. P-DISTRIBUTION ALMOST PERIODIC SOLUTIONS OF SEMI-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH G-BROWNIAN MOTION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2230-2267. doi: 10.11948/20210392

Citation:

Qigui Yang, Huoxia Liu, Xiaofang Lin. P-DISTRIBUTION ALMOST PERIODIC SOLUTIONS OF SEMI-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH G-BROWNIAN MOTION[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2230-2267. doi: 10.11948/20210392

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

1.
Department of Mathematics, South China University of Technology, 510640, Guangzhou, China

Corresponding author: Email: qgyang@scut.edu.cn(Q. Yang)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 12071151)

Abstract

Abstract

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 semi-linear SDEs driven by $ G $-Brownian motion satisfying exponential dichotomy. Meanwhile, some examples are given to validate the obtained theoretical results.
- Almost periodic solution /
- semi-linear SDE /
- comparability approach /
- exponential dichotomy /
- G-Brownian motion
MSC: 92D25, 93D20, 93E03

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References

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