A numerical scheme for stochastic differential equations with distributional drift

DOI10.1016/J.SPA.2022.09.003zbMATH Open1500.65001arXiv1906.11026OpenAlexW2955744444WikidataQ115341097 ScholiaQ115341097MaRDI QIDQ2093691

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Publication date: 27 October 2022

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Abstract: In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to a fractional Sobolev space of negative regularity (a subspace of Schwartz distributions). We obtain a rate of convergence in a suitable $L^1$-norm and we implement the scheme numerically. To the best of our knowledge this is the first paper to study (and implement) numerical solutions of SDEs whose drift lives in a space of distributions. As a byproduct we also obtain an estimate of the convergence rate for a numerical scheme applied to SDEs with drift in $L^p$-spaces with $pin(1,infty)$.

Full work available at URL: https://arxiv.org/abs/1906.11026

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