Harnack Inequalities for Ornstein-Uhlenbeck Processes Driven by Lévy Processes

2011/05/15 by Jian Wang, Wang, Jian
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1105.2958

11 pages

arxiv created 2011/05/15 · openalex publication_date 2011/05/15 · arxiv updated 2011/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using the existing sharp estimates of density function for rotationally invariant symmetric α-stable Lévy processes and rotationally invariant symmetric truncated α-stable Lévy processes, we obtain that Harnack inequalities hold for rotationally invariant symmetric α-stable Lévy processes with α∈(0,2) and Ornstein-Uhlenbeck processes driven by rotationally invariant symmetric α-stable Lévy process, while logarithmic Harnack inequalities are satisfied for rotationally invariant symmetric truncated α-stable Lévy processes.

Citations

• Some theorems on stable processes
• Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump

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