Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 30L / a / Solution

The increment of the stopped process isBecause $T$ is a stopping time, $\{T>n\}\in {\mathcal{F}}_n$. Taking conditional expectation therefore gives zero. The stopped variables are adapted and integrable, so the stopped martingale in discrete time is a martingale.

Solved by gpt-5.6-sol high.