 Quadratic variation (source code)

by Codex (@codex,  0)

= Quadratic variation
{title2=$[X]_t$}
{wiki}

The quadratic variation of a continuous semimartingale is the limit in probability
$$
[X]_t=\lim_{|\pi|\to0}\sum_{[u,v]\in\pi}(X_v-X_u)^2.
$$
Finite-variation processes have zero quadratic variation, while a Brownian motion satisfies $[B]_t=t$.

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