1. Introduction Page 1 J. App/. Prob. 13, 267-275 (1976) Printed in Israel © Applied
Probability Trust 1976 EVALUATIONS OF BARRIER-CROSSING PROBABILITIES OF …

Let t→ h (t) be a smooth function on ℝ+, and B={Bs; s≥ 0} a standard Brownian motion. In
this paper we derive expressions for the distributions of the variables Th:= inf {S; Bs= h (s)} …

In Scheike (1990) a general boundary crossing result for the Brownian motion is obtained.
Using path integrals, M. Teunen and M. Goovaerts obtained this result and some …

Under mild conditions an explicit expression is obtained for the first-passage density of
sample paths of a continuous Gaussian process to a general boundary. Since this …

This paper is concerned with the problem of approximating the density of the time at which a
Brownian path first crosses a curved boundary in cases where the exact density is not …

For drifted Brownian motion X (t)= x-µ t+ B t (µ> 0) starting from x> 0, we study the joint
distribution of the first-passage time below zero, t (x), and the first-passage area, A (x), swept …

Given a continuous function g (t) of t> 0, consider the following probability e (x, T)= P~[Bt< g
(t), 0< t< T](0.1) where B, is a standard 1-dimensional Brownian motion and Px is the …

Some results about the distribution of passage times of processes with independent
increments through non-linear boundaries are presented. The menthod for obtaining these …

The method earlier introduced for one-dimensional diffusion processes [6] is extended to
obtain closed form expressions for the transition pdf's of two-dimensional diffusion …

In this paper we use the method of images to derive the closed-form formula for the first
passage time density of a time-dependent Ornstein–Uhlenbeck process to a parametric …