Well-posedness of density dependent SDE driven by α-stable process with Hölder drifts

Mingyan Wu and Zimo Hao

Stochastic Processes and their Applications, 2023, vol. 164, issue C, 416-442

Abstract: In this paper, we show the weak and strong well-posedness of density dependent stochastic differential equations driven by α-stable processes with α∈(1,2). The existence part is based on Euler’s approximation as Hao et al. (2021), while, the uniqueness is based on the Schauder estimates in Besov spaces for nonlocal Fokker–Planck equations. For the existence, we only assume the drift being continuous in the density variable. For the weak uniqueness, the drift is assumed to be Lipschitz in the density variable, while for the strong uniqueness, we also need to assume the drift being β0-order Hölder continuous in the spatial variable, where β0∈(1−α/2,1).

Keywords: Lévy process; Density dependent SDE; Heat kernel; Schauder’s estimate (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.07.016

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