On Maximum Increase and Decrease of Brownian Motion

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dc.creatorSalminen, Paavo
dc.creatorVallois, Pierre
dc.date2005-12-19
dc.date.accessioned2026-07-07T06:55:31Z
dc.date.available2026-07-07T06:55:31Z
dc.descriptionThe joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times of the infimum and the supremum before the exponential time. It is seen that an important element in our formula is the distribution of the maximum decrease for the three dimensional Bessel process with drift started from 0 and stopped at the first hitting of a given level. From the joint distribution of the maximum increase and decrease it is possible to calculate the correlation coefficient between these at a fixed time and this is seen to be -0.47936... .
dc.identifierhttps://arxiv.org/abs/math/0512440
dc.identifierhttp://arxiv.org/abs/math/0512440
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106303
dc.subjectProbability
dc.subject60J60;60J65;60G17;62P05
dc.titleOn Maximum Increase and Decrease of Brownian Motion
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