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February 23rd, 2015, 02:15 AM  #1 
Newbie Joined: Feb 2015 From: Amsterdam Posts: 3 Thanks: 0  A newbie needs urgent help in Markov chain
Hi people, I am a newbie in Markov chains and I have difficulty to solve some questions. I would appreciate very much if I get some help: 1) First question is about: I am given a sequence of U1, U2,U3,... of independent random variables, uniformly distributed on the unit interval (0,1). I am asked to describe how this sequence can be used to simulate Markov chain with state space {0,1} and transition matrix (p11,p12,p21,p22) starting in state 1. 2) Second question is about: an Markov process {Xt} with state space S={1,2,3}, and generator Q (a 3X3 size matrix), starting in state Xo=1. I am asked: a) Finding limits (t goes to infinite) lim P(Xt=j), j=1,2,3. b) Finding the mean recurrence time of state 1, i.e. finding expected value of T, where T=inf {t>J1 : Xt=1  Xo=1} and J1 denotes the time for the first jump. Thanks in advance... 

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chain, markov, newbie, stochastic, urgent 
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