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BETA VARIABLES AS TIMES SPENT IN [0, ∞[ BY CERTAIN PERTURBED BROWNIAN MOTIONS

Published online by Cambridge University Press:  01 August 1998

PHILIPPE CARMONA
Affiliation:
Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex, France. E-mail: [email protected]
FRÉDÉRIQUE PETIT
Affiliation:
Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, Tour 56, France 75252 Paris Cedex 05. E-mail: [email protected]
MARC YOR
Affiliation:
Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, Tour 56, 75252 Paris Cedex 05, France
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Abstract

The paper shows that the times spent in [0, +∞) by certain processes Y which are defined by perturbations of Brownian motion involving reflection at maxima and minima are beta distributed. This result relies heavily on Ray–Knight theorems for such perturbed Brownian motions.

Type
Notes and Papers
Copyright
The London Mathematical Society 1998

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