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