Spatial regularity of semigroups generated by Lévy type operators

2018/04/11 by Mingjie Liang, Jian Wang, Liang, Mingjie +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1804.03781

openalex publication_date 2018/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply the probabilistic coupling approach to establish the spatial regularity of semigroups associated with Lévy type operators, by assuming that the martingale problem of Lévy type operators is well posed. In particular, we can prove the Lipschitz continuity of the semigroups under Hölder continuity of coefficients, even when the Lévy kernel corresponding to Lévy type operators is singular.

Citations

• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises
• Well-posedness of the martingale problem for non-local perturbations of Lévy-type generators
• Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative Lévy Noises via Coupling
• Uniqueness in law for stable-like processes of variable order

Related

• Uniform Hölder Estimates on Semigroups Generated by Non-Local Operators of Variable Order
• L¹ semigroup generation for Fokker-Planck operators associated with general Lévy driven SDEs
• Regularity results for free Lévy processes
• Strict continuity of the transition semigroup for the solution of a well-posed martingale problem
• A Unified Approach to Coupling SDEs driven by Lévy Noise and Some Applications