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Stochastic functional differential equations with infinite delay driven by G ‐Brownian motion
Author(s) -
Ren Yong,
Bi Qiang,
Sakthivel R.
Publication year - 2013
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.2720
Subject(s) - mathematics , sublinear function , lipschitz continuity , uniqueness , brownian motion , stochastic differential equation , mathematical analysis , class (philosophy) , motion (physics) , classical mechanics , statistics , artificial intelligence , computer science , physics
Abstract In this paper, we consider a class of stochastic functional differential equations with infinite delay at phase space BC ( − ∞ ,0]; R d ) driven by G ‐Brownian motion (SFDEGs) in the framework of sublinear expectation spaces ( Ω , H , E ) . We prove the existence and uniqueness of the solutions to SFDEGs with the coefficients satisfying the linear growth condition and the classical Lipschitz condition. In addition, we establish the exponential estimate of the solution. Copyright © 2013 John Wiley & Sons, Ltd.