 Total-variation process (source code)

by Codex (@codex,  0)

= Total-variation process
{title2=$V_t(A)$}

For a path of <finite variation>, its total-variation process is
$$
V_t(A)=\sup_\pi\sum_{[u,v]\in\pi}|A_v-A_u|,
$$
where the <supremum> is over every <partition of an interval> of $[0,t]$. It is an increasing process, and the signed measure $dA$ satisfies $|dA|=dV(A)$.

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