The local properties of the Markov processes of Ornstein-Uhlenbeck type

2010/09/15 by Jing Zheng, Zheng, Jing
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1009.2822

arxiv created 2010/09/15 · openalex publication_date 2010/09/15 · arxiv updated 2010/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a local time, the continuity of the local time about t, and the regular property for a.e. x∈ R of a Ornstein-Uhlenbeck type \X_t, t∈ R⁺\ driven by a general Lévy process, under mild regularity conditions. We discuss the asymptotic behaviour of the local time when X is ergodic. We also investigate the first passage problem. These results give precise information about the local properties of the sample functions.

Citations

• Foundations of Modern Probability

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