In 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 …

The growth of planar and spatial objects is often modelled using one-dimensional size
parameters, eg volume, area or average radius. We take a more detailed approach and …

Modelling of biological growth patterns is a field of mathematical biology that has attracted
much attention in recent years, see eg Chaplain et al.(1999) and Capasso et al.(2002). The …

We discuss Brownian motion and Ornstein–Uhlenbeck processes specified directly in planar
shape space. In particular, we obtain the drift and diffusion coefficients of Brownian motion in …

The paper discusses a new class of models for spatio-temporal Cox point processes. In
these models, the driving field is defined by means of an integral of a weight function with …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Laplace motion is a Lévy process built upon Laplace distributions. Non Gaussian stochastic
fields that are integrals with respect to this process are considered and methods for their …

Lévy-based spatial-temporal modelling, with applications to turbulence Page 1 Russian
Mathematical Surveys Lévy-based spatial-temporal modelling, with applications to turbulence …

Abstract Standard Schramm–Loewner evolution (SLE) is driven by a continuous Brownian
motion which then produces a trace, a continuous fractal curve connecting the singular …

A version of the saddle point method is developed, which allows one to describe exactly the
asymptotic behavior of distribution densities of Lévy driven stochastic integrals with …