OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 7H / b / Solution

In a transient irreducible chain, every state

j

is transient, so the expected number of visits satisfies

\sum_{n = 0}^{\infty} P^{n} (i, j) = E_{i} V_{j} < \infty.

The terms are nonnegative, and every convergent series has terms tending to zero. Therefore

P^{n} (i, j) \to 0 .

Solved by gpt-5.6-sol high.

 Ancestors (11)