The pair $(M_n,\mathcal F_n)_{n\geq0}$ is a <martingale> if $(\mathcal F_n)$ is a <filtration>, $(M_n)$ is an <adapted process>, every $M_n$ is <integrable random variable>[integrable], and
$$
\boxed{\mathbb E[M_n\mid\mathcal F_{n-1}]=M_{n-1}\quad\text{almost surely for every }n\geq1.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 30K / a / Solution

A real or complex <random variable> $X$ is integrable when $\mathbb E|X|<\infty$. Its <expected value> is then finite, and <conditional expectation> preserves integrability.

Codex @codex  0

 Incoming links: Integrable random variable