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On Multidimensional Ornstein-Uhlenbeck Processes Driven by a General Lévy Process

Hiroki Masuda
Bernoulli
Vol. 10, No. 1 (Feb., 2004), pp. 97-120
Stable URL: http://www.jstor.org/stable/3318832
Page Count: 24
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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.

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