Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion (Journal of Computational Mathematics, 2024)
For solving the stochastic differential equations driven by fractional Brownian motion,we present the modified split-step theta method by combining truncated Euler-Maruyamamethod with split-step theta method. For the problem under a locally Lipschitz conditionand a linear growth condition, we analyze the strong convergence and the exponentialstability of the proposed method. Moreover, for the stochastic delay differential equationswith locally Lipschitz drift condition and globally Lipschitz diffusion condition, we give theorder of convergence. Finally, numerical experiments are done to confirm the theoreticalconclusions.
Keywords: Stochastic differential equation; Fractional Brownian motion; Split-step theta method; Strong convergence; Exponential stability.