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Construction of first-passage-time densities for a diffusion process which is not necessarily time-homogeneous

Published online by Cambridge University Press:  14 July 2016

R. Gutiérrez Jáimez ,
A. Juan Gonzalez  and
P. Román Román
R. Gutiérrez Jáimez
Affiliation:
Universidad de Granada
A. Juan Gonzalez
Affiliation:
Universidad de Granada
P. Román Román*
Affiliation:
Universidad de Granada
*
∗ Postal address for all authors: Department de Estadistica e Investigación Operativa, Universidad de Granada, Campus de Fuente Nueva, 18071 Granada, Spain.
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Abstract

In Giorno et al. (1988) a new method for constructing first-passage-time probability density functions is outlined. This rests on the possibility of constructing the transition p.d.f. of a new time-homogeneous diffusion process in terms of a preassigned transition p.d.f. without making use of the classical space-time transformations of the Kolmogorov equation (Ricciardi (1976)).

In the present paper we give an extension of this result to the case of a diffusion process X(t) which is not necessarily time-homogeneous, and a few examples are presented.

Keywords

TIME-NON-HOMOGENEOUS DIFFUSION PROCESSFIRST-PASSAGE-TIME DENSITIESWIENER PROCESSLOGNORMAL PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 903 - 909
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Giorno, V., Nobile, A. G. and Ricciardi, L. M. (1988) A new approach to the construction of first-passage-time densities. Cybernet. Syst. 88, 375–381.Google Scholar
[2] Ricciardi, L. M. (1976) On the transformation of diffusion processes into the Wiener process. J. Math. Anal. Appl. 54, 185–199.10.1016/0022-247X(76)90244-4Google Scholar
[3] Ricciardi, L. M. (1977) Diffusion Processes and Related Topics in Biology. Lecture Notes in Biomathematics 14, Springer-Verlag, Berlin.10.1007/978-3-642-93059-1Google Scholar