We propose an approach to compute the boundary crossing probabilities for a class of
diffusion processes which can be expressed as piecewise monotone (not necessarily one-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 …

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

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 …

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 …

We consider the boundary crossing problem for time-homogeneous diffusions and general
curvilinear boundaries. Bounds are derived for the approximation error of the one-sided …

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 …

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 …

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

Let $ X (t) $ be a stationary Gaussian process, $ f (t) $ a continuous function, and $ T $ a
finite or infinite interval. This paper develops asymptotic estimates for $ P (X (t)\geqslant f (t) …