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...Miranda holmes cerfon applied stochastic analysis spring lecture markov chains i readings strongly recommended grimmett and stirzaker optional hayes for a lively history gentle introduction to koralov sinai pp more mathematical acanonical reference on is norris wewillbeginbydiscussingmarkovchains inlectures wewilldiscussdiscrete timemarkovchains will cover continuous time setup denitions weconsider discrete space process which we write as x t thestatespacesisdiscrete e niteorcountable sowecanletitbeasetofintegers asins n or s denition the chain if it satises property p thequantities j arecalledthetransition probabilities in general transition probabili ties are functions of convenient them matrix at pij th element entries non negative ii rows sum anymatrixthatsatises above called hence stochas tic exercise show that satisfy then m any...