A numerical scheme for stochastic differential equations with distributional drift

Autor:	De Angelis, Tiziano, Germain, Maximilien, Issoglio, Elena
Rok vydání:	2019
Předmět:	Mathematics - Probability Mathematics - Numerical Analysis 65C30 (Primary) 60H35 65C20 46F99 (Secondary)
Druh dokumentu:	Working Paper
DOI:	10.1016/j.spa.2022.09.003
Popis:	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 $p\in(1,\infty)$. Comment: 34 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.11026 Zobrazit plný text záznamu View this record from Arxiv