Lévy-based growth models

Mathematics – Statistics Theory

Scientific paper

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Published in at http://dx.doi.org/10.3150/07-BEJ6130 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6130

In the present paper, we give a condensed review, for the nonspecialist reader, of a new modelling framework for spatio-temporal processes, based on L\'{e}vy theory. We show the potential of the approach in stochastic geometry and spatial statistics by studying L\'{e}vy-based growth modelling of planar objects. The growth models considered are spatio-temporal stochastic processes on the circle. As a by product, flexible new models for space--time covariance functions on the circle are provided. An application of the L\'{e}vy-based growth models to tumour growth is discussed.

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