INPUTS

P(i,j)

transition probability from state $i$ to state $j$. P must be an irreducible stochastic matrix, which means that the sum of each row must be 1 ($\backslash sum\_j=1^N\; P\_i\; j\; =\; 1$), and the rank of P must be $N$.

OUTPUTS

M(i,j)

For all $1\; \le \; i,\; j\; \le \; N$, $i\; \backslash neq\; j$, M(i,j) is the average number of transitions before state j is entered for the first time, starting from state i. M(i,i) is the $mean\; recurrence\; time$ of state $i$, and represents the average time needed to return to state i.

REFERENCES

• Grinstead, Charles M.; Snell, J. Laurie (July 1997). Introduction to Probability, Ch. 11: Markov Chains. American Mathematical Society. ISBN 978-0821807491.

See also: ctmcfpt