Let $B_t$ be a Brownian motion for a given probability space and $T:=\inf \lbrace t\geq 0 : \vert B_t \vert = 1 \rbrace$.
Is the process at this time, $B_T$, independent of the hitting time $T$? If so, how can one show this?
Independence of Brownian motion at hitting time from that hitting time
madison54
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