 Covariance identity for continuous square-integrable martingales (source code)

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= Covariance identity for continuous square-integrable martingales
{title2=$\mathbb E[M_tN_t]=\mathbb E[M,N]_t$}

For two zero-starting continuous martingales square-integrable at time $t$, the <Itô isometry> gives $\mathbb E(M_t\pm N_t)^2=\mathbb E[M\pm N]_t$. The <polarization identity> yields the displayed identity. Integrability of the cross-bracket follows from the <Kunita-Watanabe inequality> and the <Cauchy-Schwarz inequality>.

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