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Problems in Markov chains - ku

Problems inMarkov chainsDepartment of Mathematical SciencesUniversity of CopenhagenApril 2008 This collection of Problems was compiled for the course Statistik 1B. It con-tains the Problems in Martin Jacobsen and Niels Keiding: Markovk der(KUIMS 1990), and 1990 Torben MartinussenJan W. NielsenJesper MadsenIn this edition a few misprints have been correctedSeptember 1992S ren Feodor NielsenIn this edition a few misprints have been correctedSeptember 1993 Anders BrixTranslated into English. A number of additional Problems have been 2007 Merete Grove JacobsenS ren Feodor NielsenMisprints corrected and additional Problems 2008S ren Feodor Nielsen21.

Problem 3.1 Below a series of transition matrices for homogeneous Markov chains is given. Draw (or sketch) the transition graphs and examine whether the chains are irreducible. Classify the states. (a) 1 0 0 0 1 0 1/3 1/3 1/3 (b) 0 1/2 1/2 1 0 0 1 0 0 (c) 0 1 …

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