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 is an element of(1, infinity).(c) 2022 Elsevier B.V. All rights reserved.
A numerical scheme for stochastic differential equations with distributional drift
Tiziano De Angelis;Elena Issoglio
2022-01-01
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 is an element of(1, infinity).(c) 2022 Elsevier B.V. All rights reserved.
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