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Problèmes de premier passage résolubles par la méthode de séparation des variables

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Mario Lefebvre
Mario Lefebvre*
Affiliation:
École Polytechnique de Montréal
*
∗ Adresse postale: Département de mathématiques appliquées, École Polytechnique de Montréal, C. P. 6079, Succursale Centre-ville, Montréal, Québec, Canada H3C 3A7.
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Abstract

In this paper, bidimensional stochastic processes defined by ax(t) = y(t)dt and dy(t) = m(y)dt + [2v(y)]1/2 dW(t), where W(t) is a standard Brownian motion, are considered. In the first section, results are obtained that allow us to characterize the moment-generating function of first-passage times for processes of this type. In Sections 2 and 5, functions are computed, first by fixing the values of the infinitesimal parameters m(y) and v(y) then by the boundary of the stopping region.

Keywords

HITTING TIMESBIDIMENSIONAL PROCESSESSEPARATION OF VARIABLES

MSC classification

Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 60J60: Diffusion processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 337 - 348
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Recherche subventionnée par le Conseil de recherches en sciences naturelles et en génie du Canada et par le fonds FCAR du Québec.

References

Références

Abramowitz, M. Et Stegun, I. A. (1965) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York.Google Scholar
Capocelli, R. M. Et Ricciardi, L. M. (1972) On the inverse of the first passage time probability problem. J. Appl. Prob. 9, 270–287.Google Scholar
Ditkin, V. A. Et Prodnikov, A. P. (1965) Integral Transforms and Operational Calculus. Pergamon Press, Oxford.Google Scholar
Lefebvre, M. (1989) First-passage densities of a two-dimensional process. SIAM J. Appl. Math. 49, 1514–1523.Google Scholar
Lefebvre, M. (1991) Quelques résultats au sujet des densités de premier passage pour des processus de diffusion. Ann. Sci. math. Québec 15, 165–175.Google Scholar
Rishel, R. (1991) Controlled wear processes: modeling optimal control. IEEE Trans. Autom. Control 36, 1100–1102.Google Scholar
Whittle, P. (1982) Optimization over Time, Vol. I. Wiley, Chichester.Google Scholar