matlabmarkov-chainsmarkovstochastic-process

Ergodic Markov chain stationary distribution: solving eqns

I am trying to solve a set of equations to determine the stationary distribution of an ergodic Markov matrix.

Namely, the matrix is 

P=[0   0   0   0.5 0   0.5;
   0.1 0.1 0   0.4 0   0.4;
   0   0.2 0.2 0.3 0   0.3;
   0   0   0.3 0.5 0   0.2;
   0   0   0   0.4 0.6 0;
   0   0   0   0   0.4 0.6];

and the set of equations are the ones from the theorem below

How can I convert the equations above into valid Matlab syntax?

Solution

  • The stationary distribution is given by the left eigen vector with eigen-value 1.

    >> [V D] = eig( P.' ); %// note the transpose .' - we are looking for the **left** EV
>> st = V(:,1).'; %//' the stationary distribution
st =
 0.0051    0.0509    0.2291    0.6110    0.5346    0.5346
>> D(1)
 1.0000