Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 18H / a / ii

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- Solution ii

Solution

The renewal-reward form of Kac's lemma says that the expected number of visits to state

i

during one return cycle from

k

to

k

is

\frac{π _{i}}{π _{k}} .

Here time spent means the number of discrete time instants at which the chain occupies

i

between consecutive visits to

k

.

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