Uniqueness for the martingale problem associated with pure jump processes of variable order

2007/12/26 by Huili Tang, Tang, Huili · 1 citation
Mathematics · #60J75 #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0712.4137

openalex publication_date 2007/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be the operator defined on C² functions by L f(x)=∫[f(x+h)-f(x)-1_{(|h|≤ 1)}∇ f(x)⋅ h]\fracn(x,h)|h|^d+α(x)dh. This is an operator of variable order and the corresponding process is of pure jump type. We consider the martingale problem associated with L. Sufficient conditions for existence and uniqueness are given. Transition density estimates for α-stable processes are also obtained.

Cited by

• Uniform Hölder Estimates on Semigroups Generated by Non-Local Operators of Variable Order
• A new technique for proving uniqueness for martingale problems

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