A new computationally simple, speedy and accurate method is proposed to construct first-
passage-time probability density functions for Gauss–Markov processes through time …

We show a lower bound for the boundary crossing probability P {∃ z∈[0, 1]: h (z)+ B0 (z)> u
(z)} with B0 a Brownian bridge, ha trend function and ua boundary function. By that we get …

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 …

Under some weak conditions, the first-passage time of the Brownian motion to a continuous
curved boundary is an almost surely finite stopping time. Its probability density function (pdf) …

The paper describes a new numerical method for the calculation of noncrossing
probabilities for arbitrary boundaries by a Poisson process. We find the method to be simple …

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments
through a constant boundary is considered under the assumption that the time intervals …

The first-passage-time pdf through a time-dependent boundary for one-dimensional
diffusion processes is proved to satisfy a new Volterra integral equation of the second kind …

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 …

The first-passage problem for the one-dimensional Wiener process with drift in the presence
of elastic boundaries is considered. We use the Kolmogorov backward equation with …

We consider a bivariate Gauss–Markov process and we study the first passage time of one
component through a constant boundary. We prove that its probability density function is the …