 Solution

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

π = (π_{i})_{i \in S}

with total mass one that is preserved by one transition:

π_{i} \geq 0, i \in S \sum π_{i} = 1, π_{j} = i \in S \sum π_{i} P_{ij} (j \in S) .

In matrix notation,

π P = π

. If the initial state has distribution

π

, so does the state at each later time.

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