Non UBC
DSpace
Groeneboom, Piet
2018-07-29T05:00:16Z
2018-01-29T09:14
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.
https://circle.library.ubc.ca/rest/handle/2429/66600?expand=metadata
43 minutes
video/mp4
Author affiliation: TUDelft
Banff (Alta.)
10.14288/1.0369233
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Statistics
Operations research, mathematical programming
Chernoff's distribution and differential equations of parabolic and Airy type
Moving Image
http://hdl.handle.net/2429/66600