※ 引述《jenban (点滴)》之铭言： : 2008 Operation Research 2 : Assignment 8 : Due day: : 2008/04/28 : Problems: : 1) Consider he Markov chain that has the following (one-step) : transition matrix. : 0 1 2 3 4 : 0 ┌ 0 4/5 0 1/5 0 ┐ : 1 │1/4 0 1/2 1/4 0 │ : P= 2 │ 0 1/2 0 1/10 2/5│ : 3 │ 0 0 0 1 0 │ : 4 └1/3 0 1/3 1/3 0 ┘ : (a) Determine the classes of this Markov chain and, for each : class, determine whether it is recurrent or transient. : (b) For each of the classes identified in part (a), determine : the period of the states in that class. Period: The period of state i is defined to be the integer t (t>1) such that (n) p =0 for all values of n other than t, 2t, 3t,… and t is the largest ii integer with this property. : 2) A transition matrix P is said to be doubly stochastic if : the sum over each column equals 1; that is : sum(i=0 to i=M)Pij=1 for all j : If such a chain is irreducible, aperiodic, and consists of M+1 : states, show that : πj=1/(M+1) for j=0,1,...,M : (n) : (postscript: Lim{p }=πj) : n->inf ij : 注意: 请用A4纸张作答，不用A4作答不予计分,并在作业的最上方标明 : 「学号」及「姓名」。 --

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