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Nonlocal stochastic differential equations with time‐varying delay driven by G ‐Brownian motion
Author(s) -
Yin Wensheng,
Cao Jinde
Publication year - 2019
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.5912
Subject(s) - mathematics , stochastic differential equation , uniqueness , brownian motion , lyapunov function , mathematical analysis , differential equation , comparison theorem , class (philosophy) , fixed point theorem , geometric brownian motion , diffusion process , nonlinear system , knowledge management , statistics , physics , innovation diffusion , quantum mechanics , artificial intelligence , computer science
This article studies a class of nonlocal stochastic differential equations driven by G ‐Brownian motion ( G ‐NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G ‐Lyapunov functional and ψ ‐type function.