# Stationary Probabilities

A transition probability matrix $P$ is said to be doubly stochastic, if each column sum is 1;that is if

$\displaystyle\sum_i P_{i,j} = 1$ for all j

If such a chain is irreducible and have states $1,...,m$, how to find its stationary probabilities?

How to answer this question. I know irreducible markov-chain in which each state can communicate with each other. All the states in the irreducible markov chain are positive recurrent.If these states are ergodic, how to find its stationary probabilities?

• You need to add the self-study tag and indicates your background on Markov chains, since you have obviously not taken a course or read an introductory book on that subject. – Xi'an Feb 11 '17 at 13:49
• @Xi'an,As far as Markov chains are concerned, I know simple random walk, gambler's ruin problem, periodic and aperiodic markov chains and transient and recurrent markov chain. – Dhamnekar Winod Feb 11 '17 at 14:03