Questions related to Brownian motion, a continuous stochastic process denoted by $W_t$, $t\geq 0$, with independent increments, such that $W(t)-W(s)$ is normally distributed, with $0$ mean and variance $t-s$.

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Brownian motion stopped at the hitting time of an independent Brownian Motion

While I was working on the exit time of planar BM out of a square I came across the following observation, which I cannot grasp. I define this exit time as $$\tau = \inf\{t \geq 0: \lvert B(t)\rvert ...