L\'{e}vy-based growth models

TL;DR

This paper reviews a new Le9vy-based framework for modeling spatio-temporal growth processes, demonstrating its potential in stochastic geometry, spatial statistics, and applications like tumor growth modeling.

Contribution

It introduces a novel Le9vy-based approach for spatio-temporal growth modeling on the circle, including new covariance models and an application to tumor growth.

Findings

Development of flexible space--time covariance functions on the circle

Application of Le9vy models to tumor growth analysis

Demonstration of the approach's potential in stochastic geometry

Abstract

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.