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Nonlocal stochastic functional differential equations driven by G‐Brownian motion and mean random dynamical systems
Author(s) -
Chen Zhang,
Yang Dandan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6480
Subject(s) - mathematics , stochastic differential equation , brownian motion , nonlinear system , uniqueness , dynamical systems theory , mathematical analysis , stochastic partial differential equation , phase space , geometric brownian motion , moment (physics) , differential equation , statistical physics , classical mechanics , diffusion process , physics , knowledge management , statistics , innovation diffusion , quantum mechanics , computer science , thermodynamics
In this paper, we consider a class of nonlocal stochastic functional differential equations driven by G‐Brownian motion (GNSFDEs) at phase space B C ( ( − ∞ , 0 ] ; R n ) whose coefficients are dependent on the p ‐th moment. Existence and uniqueness of solutions for GNSFDEs are investigated by virtue of theory of nonlinear expectation. Furthermore, we show that the solution map of GNSFDEs can generate a p ‐mean random dynamical system in nonlinear expectation framework. In addition, two examples are provided to illustrate the effectiveness of the obtained results