On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process

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Abstract

We prove the following probabilistic properties of a multidimensional Ornstein-Uhlenbeck process driven by a general Lévy process, under mild regularity conditions: the strong Feller property; the existence of a smooth transition density; and the exponential β-mixing property. As a class of possible invariant distributions of an Ornstein-Uhlenbeck process, we also discuss centred and non-skewed multidimensional generalized hyperbolic distributions.

Original languageEnglish
Pages (from-to)97-120
Number of pages24
JournalBernoulli
Volume10
Issue number1
DOIs
Publication statusPublished - Feb 1 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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