Semi-implicit Taylor schemes for stiff rough differential equations

2020/06/24 by Sebastian Riedel, Yue Wu, Riedel, Sebastian +1
Engineering · Mathematics · #60G15 #60H10 #60L20 #60L70 #65C30 #65L04 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2006.13689

openalex publication_date 2020/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Short proof of a discrete gronwall inequality
• An inequality of the Hölder type, connected with Stieltjes integration

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