A numerical scheme for stochastic differential equations with distributional drift

Tiziano De Angelis, Maximilien Germain and Elena Issoglio

Stochastic Processes and their Applications, 2022, vol. 154, issue C, 55-90

Abstract: In this paper we introduce 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 convergence rate in a suitable L1-norm and, as a by-product, a convergence rate for a numerical scheme applied to SDEs with drift in Lp-spaces with p∈(1,∞).

Keywords: Euler–Maruyama numerical scheme; Stochastic differential equations; Distributional drift; Rate of convergence; Haar and Faber functions; Fractional Sobolev spaces (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2022.09.003

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