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Four interesting problems concerning Markovian shape sequences

Part of: Distribution theory - Probability Geometric probability and stochastic geometry Markov processes

Published online by Cambridge University Press:  01 July 2016

Richard Cowan  and
Francis K. C. Chen
Richard Cowan*
Affiliation:
University of Sydney
Francis K. C. Chen*
Affiliation:
University of Hong Kong
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: rcowan@mail.usyd.edu.au
∗∗ Postal address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

In earlier work, we investigated the dynamics of shape when rectangles are split into two. Further exploration, into the more general issues of Markovian sequences of rectangular shapes, has identified four particularly appealing problems. These problems, which lead to interesting invariant distributions on [0,1], have motivating links with the classical works of Blaschke, Crofton, D. G. Kendall, Rényi and Sulanke.

Keywords

Invariant distributionsshapestochastic geometrydistribution theoryMarkov processesdynamical systemsBrownian motion

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60E05: Distributions 60J05: Discrete-time Markov processes on general state spaces
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 31 , Issue 4 , December 1999 , pp. 954 - 968
Copyright
Copyright © Applied Probability Trust 1999 

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References

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