Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Entire DC Network
Ergodic Properties Of Markov Processes, L Rey-Bellet
Ergodic Properties Of Markov Processes, L Rey-Bellet
Luc Rey-Bellet
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 …