On the distribution of the Brownian motion process on its way to hitting zero
Konstantin Borovkov, University of Melbourne
Abstract
We present functional versions of recent results on the univariate distributions of the
process Vx,u = x + W uτ(x) , 0 ≤ u ≤ 1, where W• is the standard Brownian motion
process, x > 0 and τ(x) = inf{t > 0 : Wt = -x}.
P. Billingsley.
Convergence of Probability Measures.
Wiley, New York, second edition, 1999. Math. Review 1700749
A.N. Borodin, P. Salminen.
Handbook of Brownian motion - facts and formulae.
Birkhäuser Verlag, Basel, second edition, 2002. Math. Review 1912205
K. Borovkov, A.N. Downes. On boundary crossing probabilities for
diffusion processes. Stoch. Proc. Appl. 120(2): 105--129, 2010.
Math. Review 2576883
R.T. Durrett, D. L. Iglehart, D.R. Miller.
Weak convergence to Brownian meander and Brownian excursion.
Ann. Probab. 5(1):117--129, 1977.
Math. Review 0436353
P. Chigansky, F.C. Klebaner.
Distribution of the Brownian motion on its way to hitting zero.
Electr. Comm. Probab. 13:641--648, 2008. MR
Math. Review 2466191