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

1. Jan 24, 2013

### sam48

Hi,

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. Mar 1, 2013

Re: how to compute stationary distribution for martrix with more than

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. Mar 1, 2013

### bpet

Re: how to compute stationary distribution for martrix with more than

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.