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A computational approach to first-passage-time problems for Gauss–Markov processes

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

E. Di Nardo ,
A. G. Nobile ,
E. Pirozzi  and
L. M. Ricciardi
E. Di Nardo*
Affiliation:
University of Basilicata
A. G. Nobile*
Affiliation:
University of Salerno
E. Pirozzi*
Affiliation:
University of Reggio Calabria
*
∗ Postal address: Dipartimento di Matematica, Università degli Studi della Basilicata, Via N. Sauro 85, 85100 Potenza, Italy.
∗∗ Postal address: Dipartimento di Matematica e Informatica, Università di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy.
∗∗∗ Postal address: Dipartimento di Informatica, Matematica, Elettronica e Trasporti, Università di Reggio Calabria, Via Graziella, 89100 Reggio Calabria, Italy.
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Abstract

A new computationally simple, speedy and accurate method is proposed to construct first-passage-time probability density functions for Gauss–Markov processes through time-dependent boundaries, both for fixed and for random initial states. Some applications to Brownian motion and to the Brownian bridge are then provided together with a comparison with some computational results by Durbin and by Daniels. Various closed-form results are also obtained for classes of boundaries that are intimately related to certain symmetries of the processes considered.

Keywords

Brownian bridgevarying boundariesDaniels boundaryVolterra integral equations

MSC classification

Primary: 60G15: Gaussian processes 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J60: Diffusion processes 60J65: Brownian motion
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 453 - 482
Copyright
Copyright © Applied Probability Trust 2001 

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