The Dirichlet problem for stable-like operators and related probabilistic representations

@inproceedings{Arapostathis2016TheDP,
  title={The Dirichlet problem for stable-like operators and related probabilistic representations},
  author={Ari Arapostathis and Anup Biswas},
  year={2016}
}
We study stochastic di erential equations with jumps with no di usion part, governed by a large class of stable-like operators, which may contain adrift term. For this class of operators,weestablish the regularity of solutions to the Dirichlet problem up to the boundary as well as the usual stochastic characterization of these solutions. We also establish key connections between the recurrence properties of the jumpprocess and the associated nonlocal partial di erential operator. Provided that… CONTINUE READING