Two explicit methods for one-sided Lipschitz stochastic differential equations driven by fractional Brownian motion

Abstract

For solving the stochastic differential equations with the one-sided Lipschitz and polynomial increasing drift coefficients driven by fractional Brownian motion, we propose the tamed Euler–Maruyama method and the explicit Euler–Maruyama method with projection. By using the modified coefficients, the errors of these two explicit methods are analyzed recursively and the convergence rates are obtained. A numerical experiment is carried out to support our theoretical results.