2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212084In the present paper, we give a condensed review, for the nonspecialist reader, of a new modelling framework for spatio-temporal processes, based on Lévy theory. We show the potential of the approach in stochastic geometry and spatial statistics by studying Lévy-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 Lévy-based growth models to tumour growth is discussed.Published in at http://dx.doi.org/10.3150/07-BEJ6130 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)Statistics Theorytext