The convergence of exponential Euler method for weighted fractional stochastic equations

‎In this paper‎, ‎we propose an exponential Euler method to approximate the solution of a stochastic functional differential equation driven by weighted fractional Brownian motion B^{ a‎, ‎b} under some assumptions on a and b‎. ‎We obtain also the convergence rate of the method to the true solution after proving an L^{ ۲}-maximal bound for the stochastic integrals in this case‎.

Keywords:

Malliavin calculus , Stochastic differential equations , Weighted fractional Brownian motion , Exponential Euler scheme