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Markov Chains and Applications - University of Chicago

MarkovChainsandApplicationsAlexanderVolf ovskyAugust17,2007 AbstractInthispap erIprovideaquickoverviewofSto chasticpro ,probability, chasticpro ,IwouldliketothankSamRaskinforinspiratio nalconversationswhenthepap erseemedtob o okthatisusedinorderto ndstatementsofsomeofthetheoremsistherefe renceguidebyLarryWasserman,Al ductionInadeterministicworld,itisgo o dtoknowthatsometimesrandomnesscanstillo chasticpro cessistheexactopp ositeofadeterministicone,andisarandompro cessandthefunctionbywhichitisde ned,wecansp eakoflikelyoutcomesofthepro chasticpro nesMarkovchainsandgo esthroughtheirmainprop ertiesaswellassomeinterestingexamplesoft heactionsthatcanb ep erbydrawingonanimp ortantasp ectofMarkovchains:theMarkovchainMonteCar lo(MCMC)metho ,Section3employsimp ortancesamplinginordertodemonstratethep chasticpro cessesthathavetheMarkovProp erty, nitionofMarkovProp ertyInformallyitistheconditionthatgivena state,thepastandfuturestatesareindep neitasfol

Markov Chains and Applications Alexander olfoVvsky August 17, 2007 Abstract In this paper I provide a quick overview of Stochastic processes and then quickly delve into a discussion of Markov Chains.

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