| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2717 - 2738 | |
| DOI | https://doi.org/10.1051/m2an/2025064 | |
| Published online | 29 September 2025 | |
Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space
1
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
2
Department of Mathematics “G. Peano”, University of Turin, Via Carlo Alberto 10, 10123 Torino, Italy
* Corresponding author: elena.issoglio@unito.it
Received:
13
October
2023
Accepted:
10
July
2025
This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function in the spatial variable, in particular being a ½-Hölder continuous function of time taking values in a Hölder-Zygmund space C−γ of negative order −γ < 0. We design an Euler– Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong L1 convergence rate. We finally implement the scheme and discuss the results obtained.
Mathematics Subject Classification: Primary 65C30 / Secondary 60H35 / 65C20 / 46F99
Key words: Distributional drift / Euler–Maruyama scheme / rate of convergence / Besov space / stochastic differential equation / numerical scheme
© The authors. Published by EDP Sciences, SMAI 2025
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