Regularity of density for SDEs driven by degenerate Lévy noises

2014/01/19 by Yulin Song, Xicheng Zhang, Song, Yulin +1
Economics, Econometrics and Finance · Mathematics · #60H07 #60H10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60H07 #msc:60H10

paper · pdf · doi:10.48550/arxiv.1401.4624

25 pages

arxiv created 2014/01/19 · openalex publication_date 2014/01/19 · arxiv updated 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using Bismut's approach about the Malliavin calculus with jumps, we study the regularity of the distributional density for SDEs driven by degenerate additive Lévy noises. Under full Hörmander's conditions, we prove the existence of distributional density and the weak continuity in the first variable of the distributional density. Under the uniform first order Lie's bracket condition, we also prove the smoothness of the density.

Citations

• Nonlocal Hormander's hypoellipticity theorem
• Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity

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• Smooth densities of stochastic differential equations forced by degenerate stable type noises

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