Related papers: On Spatial Point Processes with Uniform Births and…
This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…
We study a general class of birth-and-death processes with state space $\mathbb{N}$ that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is…
In this paper, we study the expected value of the pair correlation statistics of randomized point configurations on the sphere, with the emphasis on point configurations generated by determinantal point processes. We study the cases of the…
We provide necessary and sufficient conditions for explosion and implosion of birth-and-death (non-Markov) continuous-time random walks. In other words, we obtain conditions for $\infty$ to be accessible and for it to be an entrance point.…
This paper is concerned with the characterizations of fixed points of the generating function of branching processes with countably infinitely many types. We assume each particle of type $i$ can only give offspring of type $j\geq i$, whose…
We consider a simple model of a one dimensional universe embedded in the Euclidean plane. In this model, a circle travelling at constant speed intersects the line in a pair of points which first separate and then rejoin. We interpret this…
We study the interface of the multitype contact process on $\mathbb{Z}$. In this process, each site of $\mathbb{Z}$ is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established…
We study a collection of self-propelled polar particles on a two-dimensional substrate with birth and death. We introduce a minimal lattice model for the system using active Ising spins, where each particle can have two possible…
Consider a symmetrical conflict relationship between the points of a point process. The Mat\'ern type constructions provide a generic way of selecting a subset of this point process which is conflict-free. The simplest one consists in…
We study the positive recurrence of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a…
Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
Let $\omega=(\omega_i)_{i\in\mathbb Z}=(\mu^{L}_i,...,\mu^{1}_i,\lambda_i)_{i\in \mathbb Z}$, which serves as the environment, be a sequence of i.i.d. random nonnegative vectors, with $L\ge1$ a positive integer. We study birth and death…
We study a spatial birth-and-death process on the phase space of locally finite configurations $\Gamma^+ \times \Gamma^-$ over $\mathbb{R}^d$. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck…
The fractional birth and the fractional death processes are more desirable in practice than their classical counterparts as they naturally provide greater flexibility in modeling growing and decreasing systems. In this paper, we propose…
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…
In this article, we consider a generalisation of the spatial Muller's ratchet introduced by Foutel-Rodier and Etheridge. This particle system is a spatial model of an asexual population, with birth and death rates that depend on the local…