PITMAN, J. and YOR, M., The law of a maximum of a Bessel bridge, Electronic J. Probability 4 (1999), Paper no. 15, 1-35. The law of a maximum of a Bessel bridge Electronic J. Probability
Abstract
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t ↦ a + bt, a ≥ 0, b ∈ ℝ, by a reflecting Brownian motion. The main tool hereby is Doob’s formula which gives the probability that Brownian motion started inside a wedge does not hit this wedge. Other key ingredients are the time inversion property of Brownian motion and the time reversal property of diffusion bridges. Secondly, this methodology can also be applied for the three-dimensional Bessel process. Thirdly, we consider Bessel bridges from 0 to 0 with dimension parameter δ > 0 and show that the probability that such a Bessel bridge crosses an affine boundary is equal to the probability that this Bessel bridge stays below some fixed value.
with a unit root , Econometrica 55 ( 1987 ), 277 – 301 . MR 89c:62156 [14] P itman , J. and Y or , М. , A decomposition of Bessel bridges, Z
Donati-Martin, C. , Some remarks about the identity in law for the Bessel bridge \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage
PITMAN, J. and YOR, M., A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete , 59(4) (1982), 425-457. MR 84a: 60091 A decomposition of Bessel bridges Z. Wahrsch. Verw. Gebiete
Pitman, J. and Yor, M. , A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete 59(4) (1982), 425–457. MR 84a :60091 Yor M. A decomposition of Bessel bridges
