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 …

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 …

We propose a new approach to calculating the first passage time densities for Brownian
motion crossing piecewise linear boundaries which can be discontinuous. Using this …

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 …

The two-sided nonlinear boundary crossing probabilities for one-dimensional Brownian
motion and related processes have been studied in Fu and Wu (2010) based on the finite …

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 …

~ 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 …

Using the Girsanov transformation we derive estimates for the accuracy of piecewise
approximations for one-sided and two-sided boundary crossing probabilities. We …

The problem of approximating boundary hitting times for diffusion processes, and in
particular Brownian motion, is considered. Using a combination of probabilistic and function …

Explicit formulas for the first hitting time distributions for a standard Brownian motion and
different regions including rectangular, triangle, quadrilateral and a region with piecewise …