Exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise

Abstract

We discuss a system of stochastic differential equations with a stiff linear term and additive noise driven by fractional Brownian motions (fBms) with Hurst parameter H>1/2, which arise e. g., from spatial approximations of stochastic partial differential equations. For their numerical approximation, we present an exponential Euler scheme and show that it converges in the strong sense with an exact rate close to the Hurst parameter H. Further, based on (E. Buckwar, M.G. Riedler, and P.E. Kloeden 2011), we conclude the existence of a unique stationary solution of the exponential Euler scheme that is pathwise asymptotically stable.

References in corpus (4)

• Optimal Strong Convergence Rate of a Backward Euler Type Scheme for the Cox--Ingersoll--Ross Model Driven by Fractional Brownian Motion
• Runge-Kutta Lawson schemes for stochastic differential equations
• Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants
• Stochastic B-series and order conditions for exponential integrators