Semi-implicit Taylor schemes for stiff rough differential equations

Abstract

We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the multiplicative noise case, the equation is understood as a rough differential equation in the sense of T.~Lyons. We focus on equations for which the drift coefficient may be unbounded and satisfies a one-sided Lipschitz condition only. We prove well-posedness of the methods, provide a full analysis, and deduce their convergence rate. Numerical experiments show that our schemes are particularly useful in the case of stiff rough stochastic differential equations driven by a fractional Brownian motion.

References in corpus (4)

• Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
• The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
• On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
• Symplectic Runge-Kutta Methods for Hamiltonian Systems Driven by Gaussian Rough Paths

Cited by in corpus (1)

• The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation