Related papers: Nonlinearly Perturbed Birth-Death-Type Models
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability…
We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
We show that the posterior distribution of parameters in a hidden Markov model with parametric emission distributions and discrete and known state space is asymptotically normal. The main novelty of our proof is that it is based on a…
Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity,…
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…
This paper considers hidden Markov models where the observations are given as the sum of a latent state which lies in a general state space and some independent noise with unknown distribution. It is shown that these fully nonparametric…
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured population with distributed states at birth. Hierarchical…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions…
A mixture of two or more count distributions has become deeply embedded in the analysis of excess counts, often relative to the stationary (equilibrium) distributions of birth-death processes such as the geometric, Poisson, Poisson-Lindley…
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the…
We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.
We consider a collection of Markov chains that model the evolution of multitype biological populations. The state space of the chains is the positive orthant, and the boundary of the orthant is absorbing representing the extinction states…
In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI),…