On the Coupling Property and the Liouville Theorem for Ornstein-Uhlenbeck Processes

Details On the Coupling Property and the Liouville Theorem for Ornstein-Uhlenbeck Processes On the Coupling Property and the Liouville Theorem for Ornstein-Uhlenbeck Processes

2011-04-12

arxiv.org/abs/1104.2166v2

Mathematics

Probability

21pages

Scientific paper

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.

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