Let $B_t$ be a standard brownian motion. The variation is not bounded on any interval. What if I can only detect variation of a,ie I only observe the process $[B/a]_t$. Then this is a bounded variation process. Can I explicitly calculate this variation? with the use of local times eventually? then I am thinking this behaves like $1/\sqrt{a}$, by scaling, but I can find any references. Could somebody point me in the right direction?
2026-03-27 01:44:39.1774575879
Variation of a Brownian Motion
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