 Martingale product identity (source code)

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= Martingale product identity

For continuous local martingales $M$ and $N$, the <Itô product rule> says that
$$
M_tN_t-M_0N_0-[M,N]_t
$$
is a <local martingale>. If the martingales are square-integrable and converge in $L^2$, then
$$
\mathbb E[M_\infty N_\infty]=\mathbb E[M_0N_0]+\mathbb E[M,N]_\infty.
$$

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