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How to compute stationary distribution for martrix with more than 1 closed class 
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#1
Jan2413, 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, 


#2
Mar113, 05:31 PM

HW Helper
P: 1,371

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.



#3
Mar113, 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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