Related papers: Bessel-like birth-death process
In this note we highlight the role of fractional linear birth and linear death processes recently studied in \citet{sakhno} and \citet{pol}, in relation to epidemic models with empirical power law distribution of the events. Taking…
Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing…
We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov…
Birth-and-death processes (BDPs) form a class of continuous-time Markov chains that are particularly suited to describing the changes in the size of a population over time. Population-size-dependent BDPs (PSDBDPs) allow the rate at which a…
Death events commonly arise from complex interactions among interrelated causes, formally classified in reporting practices as underlying and contributing. Leveraging information from death certificates, these interactions can be naturally…
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…
This paper presents a new view of household epidemic models, where the interaction between the households is of mean field type. We thus obtain in the limit of infinitely many households a nonlinear Markov process solution of a McKean -…
Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such processes and are processes with state space…
The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…
The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…
This paper is an attempt to formalize analytically the question raised in "World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?" Huffington Post, \cite{HJ}. We start developing simple deterministic Malthusian growth…
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein.…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…
Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
Process mining is a well-established discipline of data analysis focused on the discovery of process models from information systems' event logs. Recently, an emerging subarea of process mining, known as stochastic process discovery, has…
In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we…
It is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with…