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Ergodic properties of Markov processes
Open Quantum Systems II (2006)
  • L Rey-Bellet, University of Massachusetts - Amherst
In these notes we discuss Markov processes, in particular stochastic differential equations (SDE) and develop some tools to analyze their long-time behavior. There are several ways to analyze such properties, and our point of view will be to use systematically Liapunov functions which allow a nice characterization of the ergodic properties. In this we follow, at least in spirit, the excellent book of Meyn and Tweedie [7]. In general a Liapunov function W is a positive function which grows at infinity and satisfies an inequality involving the generator of the Markov process L: roughly speaking we have the implications (α and β are positive constants)
Publication Date
January 1, 2006
Citation Information
L Rey-Bellet. "Ergodic properties of Markov processes" Open Quantum Systems II Vol. 1881 (2006)
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