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

2014/01/23 by Ari Arapostathis, Anup Biswas, Arapostathis, Ari +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #58F11 #60J45 #60J75 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1401.6198

openalex publication_date 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Non-local gradient dependent operators
• Uniqueness of Stable Processes with Drift

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