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Beta Variables as Times Spent in [0, ∞[ By Certain Perturbed Brownian Motions
Author(s) -
Carmona Philippe,
Petit Frédérique,
Yor Marc
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006401
Subject(s) - brownian motion , maxima and minima , reflected brownian motion , mathematics , geometric brownian motion , statistical physics , brownian excursion , beta (programming language) , mathematical analysis , reflection (computer programming) , diffusion process , physics , computer science , statistics , programming language , knowledge management , innovation diffusion
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.