Quadratic covariation (source code)

= Quadratic covariation
{title2=$[M,N]_t$}

The quadratic covariation of two continuous semimartingales is the limit in probability
$$
[M,N]_t=\lim_{|\pi|\to0}\sum_{[u,v]\in\pi}(M_v-M_u)(N_v-N_u).
$$
The <polarization identity> gives $[M,N]=\frac14([M+N]-[M-N])$.

= Cross-variation
{synonym}