Simulation of first-passage times for alternating Brownian motions
A. Di Crescenzo, E. Di Nardo, L.M. Ricciardi
TL;DR
This paper develops bounds and simulation methods for the first-passage times of alternating Brownian motions crossing a boundary, with applications in environmental sciences and finance.
Contribution
It introduces new bounds and a simulation procedure for first-passage times in alternating Brownian motions, extending previous models.
Findings
Bounds for the first-passage-time density and distribution function are derived.
A simulation procedure for estimating first-passage times is constructed.
Applications demonstrate relevance in environmental sciences and financial modeling.
Abstract
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.
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