Question: 15.7 Let Xt, t 0 be defined as Xt = {Bt | Bt 0}, t > 0, where Bt is a Brownian motion.

15.7 Let Xt, t ≥ 0 be defined as Xt = {Bt | Bt ≥ 0}, ∀t > 0, where Bt is a Brownian motion. That is, the process has the paths of the Brownian motion conditioned by being positive at t.

a) Show that the pdf of Xt is fXt (x)=2fBt (x), ∀x ≥ 0.

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