A numerical scheme for stochastic differential equations with distributional drift

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 $p\in (1,\infty )$.

34 pages, 2 figures

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Cited by in corpus (5)

• Approximation of SDEs -- a stochastic sewing approach
• Quantifying a convergence theorem of Gyöngy and Krylov
• Taming singular stochastic differential equations: A numerical method
• Numerical approximation of SDEs with fractional noise and distributional drift
• Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space