※ 引述《jenban (點滴)》之銘言：
: 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: 請用A4紙張作答，不用A4作答不予計分,並在作業的最上方標明
: 「學號」及「姓名」。
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※ 編輯: jenban 來自: 140.112.110.216 (04/24 13:54)