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

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

b) Calculate E[Xt] and V(Xt).

c) Is Xt a Gaussian process?

d) Is Xt stationary?

e) Are Xt and |Bt| identically distributed?