Stochastic functional differential equations with infinite delay driven by <i>G</i>‐Brownian motion

Abstract

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 . 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 &amp; Sons, Ltd.