The first-passage density of the Brownian motion process to a curved boundary

J Durbin, D Williams - Journal of applied probability, 1992 - cambridge.org
An expression for the first-passage density of Brownian motion to a curved boundary is
expanded as a series of multiple integrals. Bounds are given for the error due to truncation …

Boundary crossing probability for Brownian motion and general boundaries

L Wang, K Pötzelberger - Journal of Applied Probability, 1997 - cambridge.org
An explicit formula for the probability that a Brownian motion crosses a piecewise linear
boundary in a finite time interval is derived. This formula is used to obtain approximations to …

Linear and nonlinear boundary crossing probabilities for Brownian motion and related processes

JC Fu, TL Wu - Journal of Applied Probability, 2010 - cambridge.org
We propose a new method to obtain the boundary crossing probabilities or the first passage
time distribution for linear and nonlinear boundaries for Brownian motion. The method also …

The first-passage density of a continuous Gaussian process to a general boundary

J Durbin - Journal of Applied Probability, 1985 - cambridge.org
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 …

Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test

J Durbin - Journal of Applied Probability, 1971 - cambridge.org
Let w (t), 0≦ t≦∞, be a Brownian motion process, ie, a zero-mean separable normal
process with Pr {w (0)= 0}= 1, E {w (t1) w (t2)}= min (t1, t2), and let a, b denote the …

A boundary-crossing result for Brownian motion

TH Scheike - Journal of Applied Probability, 1992 - cambridge.org
~ h(t»)= f!lJ ( ~ h(t») . Page 1 J.Appl.Prob.29,448-453(1992) Printed in Israel e Applied
Probability Trust 1992 A BOUNDARY-CROSSING RESULT FOR BROWNIAN MOTION THOMAS …

Boundary crossing probability for Brownian motion

K Pötzelberger, L Wang - Journal of applied probability, 2001 - cambridge.org
Wang and Pötzelberger (1997) derived an explicit formula for the probability that a Brownian
motion crosses a one-sided piecewise linear boundary and used this formula to …

Approximations of boundary crossing probabilities for a Brownian motion

A Novikov, V Frishling, N Kordzakhia - Journal of Applied Probability, 1999 - cambridge.org
Using the Girsanov transformation we derive estimates for the accuracy of piecewise
approximations for one-sided and two-sided boundary crossing probabilities. We …

Some conditional crossing results of Brownian motion over a piecewise-linear boundary

M Abundo - Statistics & probability letters, 2002 - Elsevier
Explicit formulae are found for the probability that the Brownian motion, Bt, up-crosses, in [0,
T], a piecewise-linear function S (t), with the condition that the value of Bt is assigned at a …

Approximating the first crossing-time density for a curved boundary

HE Daniels - Bernoulli, 1996 - JSTOR
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 …