Spatial regularity of semigroups generated by Lévy type operators
arXiv:1804.03781
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.
arXiv comment18 pages
References in corpus (8)
- Regularity theory for fully nonlinear integro-differential equations
- Existence and estimates of moments for Lévy-type processes
- Uniqueness of stable-like processes
- Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises
- Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative Lévy Noises via Coupling
- Uniqueness in law for stable-like processes of variable order
- Well-posedness of the martingale problem for non-local perturbations of Lévy-type generators
- Irregular Stochastic differential equations driven by a family of Markov processes