标题： 基于莱维的生长模型 显示英文标题

标题： Lévy-based growth models

摘要： 本文为非专业人士提供了一个关于基于Lévy理论的新建模框架的紧凑综述。我们通过研究平面物体的Lévy驱动增长模型，展示了该方法在随机几何和空间统计中的潜力。所考虑的增长模型是在圆上的时空随机过程。作为副产品，提出了灵活的新空间-时间圆上协方差函数模型。讨论了Lévy驱动增长模型在肿瘤生长中的应用。 显示英文摘要

摘要： 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.