WIAS Preprint No. 2734, (2020)

Semi-implicit Taylor schemes for stiff rough differential equations


  • Riedel, Sebastian

2010 Mathematics Subject Classification

  • 60G15 60H10 65C30


  • Rough paths, semi-implicit Taylor schemes, stiff systems, stochastic differential equations




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.

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