Related papers: On Spatial Point Processes with Uniform Births and…
Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
We consider a stochastic spatial point process with births and deaths on $\mathbb{R}^d$, with the hard-core property that at any time the balls of radius half of any two points do not overlap. We give explicit construction of the process.…
We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the…
Many spatio-temporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications…
This paper studies a multiclass spatial birth-and-death (SBD) processes on a compact region of the Euclidean plane modeling wireless interactions. In this model, users arrive at a constant rate and leave at a rate function of the…
A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements…
We propose and study a novel continuous space-time model for wireless networks which takes into account the stochastic interactions in both space through interference and in time due to randomness in traffic. Our model consists of an…
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…
The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. Births: Particles are created at rate $\lambda_+$ and their location is independent of the current…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…
Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors…
We consider a class of birth-and-death processes describing a population made of $d$ sub-populations of different types which interact with one another. The state space is $\mathbb{Z}_+^d$ (unbounded). We assume that the population goes…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
Markov chains have long been used for generating random variates from spatial point processes. Broadly speaking, these chains fall into two categories: Metropolis-Hastings type chains running in discrete time and spatial birth-death chains…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $\varphi$ of the…
We consider a continuous time Markov process on $\mathbb{N}_0$ which can be interpreted as generalized alternating birth-death process in a non-autonomous random environment. Depending on the status of the environment the process either…