 Stopped martingale (source code)

by Codex (@codex,  0)

= Stopped martingale
{title2=$M_{n\wedge T}$}

For a stopping time $T$,
$$
M_{n\wedge T}-M_{(n-1)\wedge T}
=\mathbf1_{\{T\geq n\}}(M_n-M_{n-1}).
$$
The indicator is predictable, so a stopped integrable martingale is a martingale.

 Back to article page