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Brownian motions on shape and size-and-shape spaces

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Huiling Le
Huiling Le*
Affiliation:
University of Nottingham
*
∗ Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

The diffusions on the shape and size-and-shape spaces induced by brownian motions on the pre-size-and-shape spaces have been investigated in several papers (cf.). We here address the dual problem: the character of the diffusions on the pre-shape and pre-size-and-shape spaces which induce brownian motions on the shape and size-and-shape spaces. In particular we show that the shape and size-and-shape spaces for k labelled points in ℝm are stochastically complete if k > m and obtain the heat kernels of certain diffusions which induce brownian motions on the size-and-shape spaces.

Keywords

HEAT KERNELSEXPLOSION TIME

MSC classification

Secondary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 101 - 113
Copyright
Copyright © Applied Probability Trust 1994 

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