Abstract
The first-passage time problem through two time-dependent boundaries
for one-dimensional Gauss-Markov processes is considered, both for fixed and for random
initial states. The first passage time probability density functions are proved to
satisfy a system of continuous-kernel integral equations that can be numerically solved
by an accurate and computationally simple algorithm. A condition on the boundaries
of the process is given such that this system reduces to a single non-singular integral
equation. Closed-form results are also obtained for classes of double boundaries
that are intimately related to certain symmetry properties of the considered processes.
Finally, the double-sided problem is considered.
