OurBigBook.comSite Source code

Stationary cycle occupation formula

For an irreducible positive-recurrent Markov chain with invariant distribution

π

, the expected number of visits to

j

during one return cycle from

i

to

i

is

\frac{π ( j )}{π ( i )} .

Combining this with the two-state excursion visit law gives

\frac{P _{i} ( T _{j} < T _{i} )}{P _{j} ( T _{i} < T _{j} )} = \frac{π ( j )}{π ( i )} .

 Ancestors (6)

 Incoming links (2)