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

The running minima satisfySince $X_{n+1}$ is independent of the past, the conditional law of $L_{n+1}$ depends only on $L_n$. Hence $(L_n)$ is a Markov chain. This is the running minimum of an independent sequence is Markov property.

Solved by gpt-5.6-sol high.