On the Distribution of the Brownian Motion Process on Its Way to Hitting Zero
نویسنده
چکیده
We present functional versions of recent results on the univariate distributions of the process Vx ,u = x +Wuτ(x), 0 ≤ u ≤ 1, where W• is the standard Brownian motion process, x > 0 and τ(x) = inf{t > 0 : Wt =−x}. Let {Wt}t≥0 be the standard univariate Brownian motion process and, for x > 0, Wx ,t := x +Wt , t ≥ 0, τ(x) := inf{t > 0 : Wx ,t = 0}. As is well known, τ(x) is a proper random variable with density
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