  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 between consecutive changes of these moments
are described by an alternating renewal process. Bounds to the
first-passage-time density and distribution function are obtained, and a
simulation procedure to estimate first-passage-time densities is constructed.
Examples of applications to problems in environmental sciences and mathematical
finance are also provided.

Probability