Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 3 / 8H / ii / Solution

For <independent random variables> with a common law, $L_n=\min_{j\leq n}X_j$ satisfies $L_{n+1}=\min(L_n,X_{n+1})$. The next-state law therefore depends on the past only through $L_n$.

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 Incoming links: Running minimum of an independent sequence is Markov