A NOTE ON THE APPROXIMATE SOLUTIONS FOR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY G-BROWNIAN MOTION

摘要

By using the Caratheodory approximation method, the current article presents the analysis of exact and approximate solutions for stochastic differential equations (SDEs) in the framework of G-Brownian motion. In view of the non-linear growth and non-Lipschitz conditions, the boundedness of the Caratheodory approximate solutions Y~q(t). q ≥ 1 in the space M_G~2([t_0,T]; R~n) has been determined. Estimate for the difference between the exact solution Y(t) and the Carathcodory approximate solutions Y~q(t) has been derived.