how to compute stationary distribution for martrix with more than 1 closed class

by sam48
Tags: class, compute, distribution, martrix, stationary
sam48 is offline
Jan24-13, 07:32 PM
P: 1

Thank you in advance if anyone can answer this question.

How any stationary distributions exists in below matrix and what are the value

.5 0 0 .5
.25 .5 .25 0
0 0 1 0
1/6 0 0 5/6

Any information regarding how to compute stationary distribution in a martrix with more than 1 closed class would be appreciated.
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statdad is offline
Mar1-13, 05:31 PM
HW Helper
P: 1,344
Your chain has an absorbing state (the third state, since the 3,3 entry is 1). Write this matrix in canonical form and analyze it with the standard methods.
bpet is offline
Mar1-13, 09:56 PM
P: 523
One way is just to solve the eigenvector equation xA=x - since your example has 2 closed classes (the other being {1,4}), there will be two LI eigenvectors. Positivity and summation to 1 will tell you which linear combinations are valid.

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