Transition probabilities of Lévy-type processes: Parametrix construction

Abstract

We present an existence result for Lévy-type processes which requires only weak regularity assumptions on the symbol $q(x,\xi )$ with respect to the space variable $x$. Applications range from existence and uniqueness results for Lévy-driven SDEs with Hölder continuous coefficients to existence results for stable-like processes and Lévy-type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy-type processes. The paper includes an extensive list of Lévy(-type) processes satisfying the assumptions of our results.

References in corpus (4)

• On Shift Harnack Inequalities for Subordinate Semigroups and Moment Estimates for Lévy Processes
• Existence and estimates of moments for Lévy-type processes
• Solutions of Lévy-driven SDEs with unbounded coefficients as Feller processes
• On weak uniqueness and distributional properties of a solution to an SDE with $\alpha$-stable noise

Cited by in corpus (1)

• Schauder estimates for Poisson equations associated with non-local Feller generators