Intrinsic Ultracontractivity for General Lévy processes on Bounded Open Sets

2015/01/25 by Xin Chen, Jian Wang, Chen, Xin +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1501.06130

openalex publication_date 2015/01/25 · arxiv created 2015/08/29 · arxiv updated 2015/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a general (not necessarily symmetric) Lévy process killed on exiting a bounded open set (without regular condition on the boundary) is intrinsically ultracontractive, provided that B(0,R₀)⊆ \rmsupp(ν) for some constant R₀>0, where \rmsupp(ν) denotes the support of the associated Lévy measure ν. For a symmetric Lévy process killed on exiting a bounded Hölder domain of order 0, we also obtain the intrinsic ultracontractivity under much weaker assumption on the associated Lévy measure.

Citations

• Intrinsic Ultracontractivity of Feynman-Kac Semigroups for Symmetric Jump Processes

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