A diffusion model for Bookstein triangle shape
UNSPECIFIED. (1998) A diffusion model for Bookstein triangle shape. ADVANCES IN APPLIED PROBABILITY, 30 (2). pp. 317-334. ISSN 0001-8678Full text not available from this repository.
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 . The computer algebra implementation Itovsn3  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|
|Number of Pages:||18|
|Page Range:||pp. 317-334|
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