 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2011/m/m5/a/ii/solution

{0, 1, \dots, N}

, with initial state

X_{1} = N

. With rows indexed by the current state and columns by the next state, the transition matrix is

P_{ij} = ⎩ ⎨ ⎧ 1, 1/ i, 0, i = j = 0, 1 \leq i \leq N, 0 \leq j < i, otherwise .

The state strictly decreases at each step until absorption at

0

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