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Smooth first-passage densities for one-dimensional diffusions

Published online by Cambridge University Press:  14 July 2016

E. J. Pauwels
E. J. Pauwels*
Affiliation:
Limburgs Universitair Centrum
*
∗Postal address: Limburgs Universitair Centrum, B-3610 Diepenbeek, Belgium. Research partially supported by NFWO (Belgium).
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Abstract

The purpose of this paper is to show that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density.

In order to be able to prove this, we shall show that Brownian motion conditioned to first hit a point at a specified time has the same distribution as a Bessel (3)-process with changed time scale.

Keywords

BESSEL (3)-PROCESSSMOOTHNESS CONDITIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 370 - 377
Copyright
Copyright © Applied Probability Trust 1987 

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References

Ikeda, N. and Watanabe, S. (1981) Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam.Google Scholar
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