UNSPECIFIED. (1998) A diffusion model for Bookstein triangle shape. ADVANCES IN APPLIED PROBABILITY, 30 (2). pp. 317-334. ISSN 0001-8678

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Abstract

A stochastic dynamical context is developed for Bookstein's shape theory. It is shown how Bookstein's shape space for planar triangles arises naturally when the landmarks are moved around by a special Brownian motion on the general linear group of invertible (2 x 2) real matrices. Asymptotics for the Brownian transition density are used to suggest an exponential family of distributions, which is analogous to the von Mises-Fisher spherical distribution and which has already been studied in [23]. The computer algebra implementation Itovsn3 [34] of stochastic calculus is used to perform the calculations (some of which actually date back to work by Dyson on eigenvalues of random matrices and by Dynkin on Brownian motion on ellipsoids). An interesting feature of these calculations is that they include the first application (to the author's knowledge) of the Grobner basis algorithm in a stochastic calculus context.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ADVANCES IN APPLIED PROBABILITY
Publisher:	APPLIED PROBABILITY TRUST
ISSN:	0001-8678
Date:	June 1998
Volume:	30
Number:	2
Number of Pages:	18
Page Range:	pp. 317-334
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/15515

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