Article
Ergodic properties of Markov processes
Open Quantum Systems II
(2006)
Abstract
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)
Disciplines
Publication Date
January 1, 2006
Citation Information
L Rey-Bellet. "Ergodic properties of Markov processes" Open Quantum Systems II Vol. 1881 (2006) Available at: http://works.bepress.com/luc_rey_bellet/16/