Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 18H / a / Solution

A stopping time $T$ has $\{T\le n\}$ determined by $X_0,\dots ,X_n$. The Strong Markov property says that, conditional on $T<\infty$ and $X_T=i$, the post-$T$ chain is a fresh chain started at $i$, independent of the pre-$T$ history.