Bernoulli

  • Bernoulli
  • Volume 10, Number 1 (2004), 97-120.

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

Hiroki Masuda

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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.

Article information

Source
Bernoulli Volume 10, Number 1 (2004), 97-120.

Dates
First available in Project Euclid: 23 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1077544605

Digital Object Identifier
doi:10.3150/bj/1077544605

Mathematical Reviews number (MathSciNet)
MR2044595

Zentralblatt MATH identifier
1048.60060

Keywords
mixing bound multidimensional generalized hyperbolic distribution operator self-decomposability Ornstein-Uhlenbeck process driven by a Lévy process

Citation

Masuda, Hiroki. On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process. Bernoulli 10 (2004), no. 1, 97--120. doi:10.3150/bj/1077544605. https://projecteuclid.org/euclid.bj/1077544605


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