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First-passage-time densities for time-non-homogeneous diffusion processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

R. Gutiérrez ,
L. M. Ricciardi ,
P. Román  and
F. Torres
R. Gutiérrez*
Affiliation:
University of Granada
L. M. Ricciardi*
Affiliation:
University of Naples
P. Román*
Affiliation:
University of Granada
F. Torres*
Affiliation:
University of Granada
*
∗Postal address: Departamento de Estadística e Investigación Operativa, Universidad de Granada, Avda. Fuentenueva s/n 18071, Granada, Spain.
∗∗Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli ‘Federico II', Via Cintia, 80126, Naples, Italy.
∗Postal address: Departamento de Estadística e Investigación Operativa, Universidad de Granada, Avda. Fuentenueva s/n 18071, Granada, Spain.
∗Postal address: Departamento de Estadística e Investigación Operativa, Universidad de Granada, Avda. Fuentenueva s/n 18071, Granada, Spain.
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Abstract

In this paper we study a Volterra integral equation of the second kind, including two arbitrary continuous functions, in order to determine first-passage-time probability density functions through time-dependent boundaries for time-non-homogeneous one-dimensional diffusion processes with natural boundaries. These results generalize those which were obtained for time-homogeneous diffusion processes by Giorno et al. [3], and for some particular classes of time-non-homogeneous diffusion processes by Gutiérrez et al. [4], [5].

Keywords

VOLTERRA INTEGRAL EQUATIONSVARYING BOUNDARIESEXOGENOUS FACTORSLOGNORMAL DIFFUSION PROCESS

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 623 - 631
Copyright
Copyright © Applied Probability Trust 1997 

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References

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