Title	Chernoff's distribution and differential equations of parabolic and Airy type
Creator	Groeneboom, Piet
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-01-29T09:14
Description	We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argument uses a relation between integrals of special functions, in particular involving integrals with respect to functions which can be called `incomplete Scorer functions'. The relation is proved by showing that both integrals, as a function of two parameters, satisfy the same extended heat equation, and the maximum principle is used to show that these solutions must therefore have the stated relation. Once this relation is established, a direct derivation of the distribution of the maximum and location of the maximum of Brownian motion minus a parabola is possible, leading to a considerable shortening of the original proofs.
Extent	43 minutes
Subject	Mathematics; Statistics; Operations research, mathematical programming
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: TUDelft
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-07-29
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0369233
URI	http://hdl.handle.net/2429/66600
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Chernoff's distribution and differential equations of parabolic and Airy type Groeneboom, Piet

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