 Solution

ID: past-exam-of-the-probability-course-of-the-university-of-oxford/2017/3/a/i/solution

P

defines an irreducible Markov chain if every state is accessible from every other state:

for every i, j \in S, there is n \geq 0 with (P^{n})_{ij} > 0.

Equivalently, all states belong to one communicating class. When

i \neq = j

, a positive number of steps is necessarily used.

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