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An introduction to Markov chains

A N D E R S TO LV E RA N I N T R O D U C T I O N TOM A R KOV C H A I N SL E C T U R E N OT E S F O R S TO C H A S T I C P R O C E S S E S2 Anders TolverDepartment of Mathematical SciencesUniversity of CopenhagenUniversitetsparken5DK-2100 Copenhagen , Denmarkemail: printing, November2016 Copyright Anders TolverISBN:978-87-7078-952-3 PrefaceThese lecture notes have been developed for the courseStochastic Pro-cessesat Department of Mathematical Sciences, University of Copen-hagen during the teaching years2010-2016. The material covers as-pects of the theory for time-homogeneous Markov chains in discreteand continuous time on finite or countable state back bone of this work is the collection of examples and exer-cises in Chapters2and3.

models for random events namely the class of Markov chains on a finite or countable state space. The state space is the set of possible values for the observations. Thus, for the example above the state space consists of two states: ill and ok. Below you will find an ex-ample of a Markov chain on a countably infinite state space, but first

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