On a Class of Stochastic Differential Equations With Jumps and Its Properties

Ari Arapostathis; Anup Biswas; Luis Caffarelli

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arXiv · 1401.6198

On a Class of Stochastic Differential Equations With Jumps and Its Properties

Ari Arapostathis·Anup Biswas·Luis Caffarelli

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Abstract

We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for a class of these operators. We also establish key connections between the recurrence properties of these jump processes and the non-local partial differential operator. One of the key results is the regularity of solutions of the Dirichlet problem for a class of operators with locally weakly Hölder continuous kernels.

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BibTeX RIS

Ari Arapostathis, Anup Biswas, Luis Caffarelli. 2015-10-05. On a Class of Stochastic Differential Equations With Jumps and Its Properties. https://arxiv.org/abs/1401.6198

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