Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space

2023/09/20 by Luis Mario Chaparro Jáquez, Jáquez, Luis Mario Chaparro, Elena Issoglio +3
Economics, Econometrics and Finance · Engineering · Mathematics · #46F99 (Secondary) #60H35 #65C20 #65C30 (Primary) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2309.11396

openalex publication_date 2023/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Hölder-Zygmund space C^-γ of negative order -γ<0 in the spatial variable. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong L¹ convergence rate. We finally implement the scheme and discuss the results obtained.

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