On the time to reach maximum for a variety of constrained Brownian motions

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dc.creatorMajumdar, Satya. N.
dc.creatorRandon-Furling, Julien
dc.creatorKearney, Michael J.
dc.creatorYor, Marc
dc.date2008-02-19
dc.date.accessioned2026-07-07T10:13:59Z
dc.date.available2026-07-07T10:13:59Z
dc.descriptionWe derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and reflected bridges associated with Brownian motion. By subsequently integrating over M, the marginal density P(t_m) is obtained in each case in the form of a doubly infinite series. For the excursion and meander, we analyse the moments and asymptotic limits of P(t_m) in some detail and show that the theoretical results are in excellent accord with numerical simulations. Our primary method of derivation is based on a path integral technique; however, an alternative approach is also outlined which is founded on certain "agreement formulae" that are encountered more generally in probabilistic studies of Brownian motion processes.
dc.descriptionSubmitted to J. Phys. A
dc.identifierhttps://arxiv.org/abs/0802.2619
dc.identifierhttp://arxiv.org/abs/0802.2619
dc.identifierJournal of Physics A Mathematical and Theoretical 41 (2008) 365005
dc.identifierdoi:10.1088/1751-8113/41/36/365005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172726
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.titleOn the time to reach maximum for a variety of constrained Brownian motions
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