Why the stationary distribution of this markov chain is empty?

Hello,

I have this probability matrix:

P = [0 1 0 0 0 0;
0 0 1 0 0 0;
0 0 0 1 0 0;
0 0 0 0 1 0;
0 0.0833333333333333 0 0 0 0.916666666666667;
1 0 0 0 0 0];

If I create a dtmc object and compute the stationary distribution as follows

mc = dtmc(P);
mu = asymptotics(mc);

the asymptotics function returns an empty array. What am I missing? Even if the mc is not ergodic shouldn't it have at least one stationary distribution?

Thank you for your time.

Answer 1

[seyed mahmoud mirkhan]

hello. i solve your problem with spectral decomposition method

stationary distribution is

0.1571 0.1714 0.1714 0.1714 0.1714 0.1571