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

sam48

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,

statdad

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

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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statdad Recognitions: Homework Help	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	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.