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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
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Total absolute variation of brownian motion, with different sampling rates
Let $X$ be your list of $n$ elements representing the Brownian motion : $X_i$ is the position at the time $i$.
Let $Y=\{X_{i+1}-X_i\}$ be the list of differences of consecutive terms. As per your cod …