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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. Conditional independenceProblem that there are functions (of sets)fzandgzsuch thatfor all setsAandBwe haveP{X A, Y B|Z=z}=fz(A)gz(B)for everyz.

This collection of problems was compiled for the course Statistik 1B. It con-tains the problems in Martin Jacobsen and Niels Keiding: Markovkæder (KUIMS 1990), and more. ... Then {Yn}n≥0 is a stochastic process with countable state space Sk, some-times refered to as the snake chain. Show that {Yn}n≥0 is a homogeneous Markov chain.

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