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On the inverse of the first hitting time problem for bidimensional processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Mario Lefebvre
Mario Lefebvre*
Affiliation:
École Polytechnique de Montréal
*
∗Postal address: Département de mathématiques et de génie industriel, École Polytechnique, C. P. 6079, Succursale Centre-ville, Montréal, Québec, Canada H3C 3A7.
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Abstract

Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t), where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinitesimal moments that correspond to the chosen moment generating function.

Keywords

INTEGRATED PROCESSESHITTING TIMEKOLMOGOROV EQUATION

MSC classification

Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 60J60: Diffusion processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 610 - 622
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada and by the fund FCAR of Québec.

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