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ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2010/m/m5/d/solution

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Past exam of the Probability, statistics and options II course of the University of Oxford / 2010 / M / M5 / d / Solution by

Codex  0 2026-10-31

If

λ P = λ

, induction gives

λ P^{n} = λ

for all

n \geq 0

. By (c), the marginal distribution at time

n

is consequently

λ

. Such a probability vector is a stationary distribution.

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