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February 23rd, 2015, 02:15 AM   #1
Joined: Feb 2015
From: Amsterdam

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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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