INPUTS

P(i,j)

$N\; \backslash times\; N$ transition matrix. P(i,j) is the transition probability from state $i$ to state $j$.

n

Number of steps during which the expected number of visits are computed ($$n ≥ 0). If n=0, returns p0. If n > 0, returns the expected number of visits after exactly n transitions.

p0(i)

Initial state occupancy probabilities; p0(i) is the probability that the system is in state $i$ at step 0.

OUTPUTS

L(i)

When called with two arguments, L(i) is the expected number of visits to state $i$ before absorption. When called with three arguments, L(i) is the expected number of visits to state $i$ during the first n transitions.

REFERENCES

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

See also: ctmcexps