On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes
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Contributors
Abstract
Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup of Ornstein-Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful coupling and the Liouville theorem for general Ornstein-Uhlenbeck processes. Then we present the explicit coupling property of Ornstein-Uhlenbeck processes directly from the behaviour of the corresponding symbol or characteristic exponent. This approach allows us to derive gradient estimates for Ornstein-Uhlenbeck processes via the symbol.
Details
Original language | English |
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Pages (from-to) | 119-140 |
Number of pages | 22 |
Journal | Journal of evolution equations |
Volume | 12 |
Issue number | 1 |
Publication status | Published - Mar 2012 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- coupling property, gradient estimates, Liouville theorem, Ornstein-Uhlenbeck processes