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

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

2010-09-15

arxiv.org/abs/1009.2822v1

Mathematics

Probability

Scientific paper

We prove the existence of a local time, the continuity of the local time about $t$, and the regular property for $a.e.$ $x\in R$ of a Ornstein-Uhlenbeck type $\{X_t,\ t\in R^+\}$ driven by a general L\'{e}vy 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.

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