Related papers: First Steps Towards an Imprecise Poisson Process

We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient…

We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…

Event occurrence is not only subject to the environmental changes, but is also facilitated by the events that have occurred in a system. Here, we develop a method for estimating such extrinsic and intrinsic factors from a single series of…

Renewal processes are zero-dimensional processes defined by independent intervals of time between zero crossings of a random walker. We subject renewal processes them to stochastic resetting by setting the position of the random walker to…

We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…

We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving…

In this article, we introduce fractional Poisson felds of order k in n-dimensional Euclidean space $R_n^+$. We also work on time-fractional Poisson process of order k, space-fractional Poisson process of order k and tempered version of…

Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…

Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…

We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on…

In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation…

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…

A Neyman-Scott process is a special case of a Cox process. The latent and observable stochastic processes are both Poisson processes. We consider a deep Neyman-Scott process in this paper, for which the building components of a network are…

In this paper we give a historical account of the development of Poisson approximation using Stein's method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on…

The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise.…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…