- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: A transition probability matrix $\mathbf{P}$ is said to be

*doubly stochastic*if the sum over each column equals one; that is,\[\sum_i P_{i,j}=1,\qquad\forall j.\]

If such a chain is irreducible and aperiodic and consists of $M+1$ states $0,1,\ldots,M$, show that the limiting probabilities are given by

\[\pi_j=\frac{1}{M+1},\quad j=0,1,\ldots,M.\]

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!