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

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sam48
#1
Jan24-13, 07:32 PM
P: 1
Hi,

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.
regards,
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statdad
#2
Mar1-13, 05:31 PM
HW Helper
P: 1,361
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
#3
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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