Related papers: Spatial birth-death-move processes : basic propert…
We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit…
In order to numerically solve high-dimensional nonlinear PDEs and alleviate the curse of dimensionality, a stochastic particle method (SPM) has been proposed to capture the relevant feature of the solution through the adaptive evolution of…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death…
We discuss general concept of Markov statistical dynamics in the continuum. For a class of spatial birth-and-death models, we develop a perturbative technique for the construction of statistical dynamics. Particular examples of such systems…
Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
Obtaining reliable and precise estimates of wildlife species abundance and distribution is essential for the conservation and management of animal populations and natural reserves. Spatial capture-recapture (SCR) models provide estimates of…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
Human activity spaces are shaped by individual mobility and the built environment, motivating statistical methods that integrate GPS observations with GIS representations of places and routes. We propose a novel methodology to estimate…
Recent analyses combining advanced theoretical techniques and high-quality data from thousands of simultaneously recorded neurons provide strong support for the hypothesis that neural dynamics operate near the edge of instability across…
Ageing's sensitivity to natural selection has long been discussed because of its apparent negative effect on individual's fitness. Thanks to the recently described (Smurf) 2-phase model of ageing we were allowed to propose a fresh angle for…
We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which…
The spatial structure of an evolving population affects which mutations become fixed. Some structures amplify selection, increasing the likelihood that beneficial mutations become fixed while deleterious mutations do not. Other structures…