Related papers: L\'{e}vy-based growth models
We study the problem of modeling and inference for spatio-temporal count processes. Our approach uses parsimonious parameterisations of multivariate autoregressive count time series models, including possible regression on covariates. We…
We consider the problem of modeling, estimating, and controlling the latent state of a spatiotemporally evolving continuous function using very few sensor measurements and actuator locations. Our solution to the problem consists of two…
In this paper we present an $L^p$-theory for the stochastic partial differential equations (SPDEs in abbreciation) driven by L\'e{}vy processes. Existence and uniqueness of solutions in Sobolev spaces are obtained. The coefficients of SPDEs…
In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…
The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the…
A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…
We study the temporal-spatial regularity properties of tamed Euler approximations for L\'evy-driven SDEs with superlinearly growing drift and diffusion coefficients. We first introduce a novel tamed Euler-type scheme and establish its…
We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…
In the recent paper \cite{Ng5} we have introduced a method of studying the multi-dimensional Kingman convolutions and their associated stochastic processes by embedding them into some multi-dimensional ordinary convolutions which allows to…
We consider the duration of discussions in face-to-face contacts and propose a stochastic model to describe it. It is based on the points of a Levy flight where the duration of each contact corresponds to the size of the clusters produced…
A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate…
The k-parent and infinite-parent spatial Lambda-Fleming Viot processes (or SLFV), introduced in Louvet (2023), form a family of stochastic models for spatially expanding populations. These processes are akin to a continuous-space version of…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…
We describe a temporal multiscale approach for the simulation of long-term processes with short-term influences involving partial differential equations. The specific problem under consideration is a growth process in blood vessels. The…
In this paper, we first explore certain structural properties of L\'evy flows and use this information to obtain the existence of strong solutions to a class of Stochastic PDEs in the space of tempered distributions, driven by L\'evy noise.…
The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the…
The time evolution of random variables with L\'evy statistics has the ability to develop jumps, displaying very different behaviors from continuously fluctuating cases. Such patterns appear in an ever broadening range of examples including…
The aim of this paper is to discuss an estimation and a simulation method in the \textsf{R} package YUIMA for a linear regression model driven by a Student-$t$ L\'evy process with constant scale and arbitrary degrees of freedom. This…
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…