Numerical approximation of SDEs with fractional noise and distributional drift

Ludovic Goudenège, El Mehdi Haress and Alexandre Richard

Stochastic Processes and their Applications, 2025, vol. 181, issue C

Abstract: We study the numerical approximation of SDEs with singular drifts (including distributions) driven by a fractional Brownian motion. Under the Catellier–Gubinelli condition that imposes the regularity of the drift to be strictly greater than 1−1/(2H), we obtain an explicit rate of convergence of a tamed Euler scheme towards the SDE, extending results for bounded drifts. Beyond this regime, when the regularity of the drift is 1−1/(2H), we derive a non-explicit rate. As a byproduct, strong well-posedness for these equations is recovered. Proofs use new regularising properties of discrete-time fBm and a new critical Grönwall-type lemma. We present examples and simulations.

Keywords: Numerical approximation; Regularisation by noise; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104533

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