Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique Access content directly
Preprints, Working Papers, ... Year : 2024

Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift

Abstract

We are interested in the discretization of stable driven SDEs with additive noise for α ∈ (1, 2) and Lq − Lp drift under the Serrin type condition α/q + d/p < α − 1. We show weak existence and uniqueness as well as heat kernel estimates for the SDE and obtain a convergence rate of order (1/α)*(α − 1 − α/q - d/p) for the difference of the densities for the Euler scheme approximation involving suitably cutoffed and time randomized drifts.
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hal-04571879 , version 1 (09-05-2024)

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Mathis Fitoussi, Benjamin Jourdain, Stéphane Menozzi. Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift. 2024. ⟨hal-04571879⟩
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