Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / M / M5 / a / ii

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- Solution ii

Solution

The state space is

{0, 1, \dots, N}

. In this increasing ordering, the transition matrix is specified by

P_{00} = 1, P_{kj} = \frac{1}{k} (k \geq 1, 0 \leq j < k), P_{kj} = 0 otherwise .

For each positive

k

, the

k

possible amounts taken correspond bijectively to the

k

possible remaining counts. Each positive-state row therefore sums to one.

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