Related papers: Consistent least squares estimation in population-…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
Hidden Markov models are versatile tools for modeling sequential observations, where it is assumed that a hidden state process selects which of finitely many distributions generates any given observation. Specifically for time series of…
Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…
In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
We introduce and study a model of long-run convention formation for rare interactions. Players in this model form beliefs by observing a recency-weighted sample of past interactions, to which they noisily best respond. We propose a…
Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…
This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M) and Wright-Fisher (WF) processes, we define a general class…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…
When a small number of individuals of organism of single species is confined in a closed space with limited amount of indispensable resources, their breading may start initially under suitable conditions, and after peaking, the population…
The controlled branching process is a generalization of the classical Bienaym\'e-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be…
We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…