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Fractional Poisson process

About: Fractional Poisson process is a(n) research topic. Over the lifetime, 868 publication(s) have been published within this topic receiving 17858 citation(s). more

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Journal ArticleDOI
TL;DR: This paper presents a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process. more

Abstract: In many stochastic models, particularly in queueing theory, Poisson arrivals both observe (see) a stochastic process and interact with it. In particular cases and/or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state. In this paper, we present a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process. more

1,177 citations

Journal ArticleDOI
Peter A. W. Lewis1, Gerald S. Shedler2Institutions (2)
Abstract: : A simple and relatively efficient method for simulating one- dimensional and two-dimensional nonhomogeneous Poisson processes is presented. The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function. In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates. more

805 citations

01 May 1997-
Abstract: Preface Introduction The Mixed Poisson Distributions Some Basic Concepts The Mixed Poisson Process Some Related Processes Cox Processes Gauss-Poisson Processes Mixed Renewal Processes Characterization of Mixed Poisson Processes Reliability Properties of Mixed Poisson Processes Characterization within Birth Processes Characterization within Stationary Point Processes Characterization within General Point Processes Compound Mixed Poisson Distributions Compound Distributions Exponential Bounds Asymptotic Behaviour Recursive Evaluation The Risk Business The Claim Process Ruin Probabilities more

342 citations

Journal ArticleDOI
Abstract: The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied examples, of the wide applicability and utility of the Chen-Stein method. These examples include birthday coincidences, head runs in coin tosses, random graphs, maxima of normal variates and random permutations and mappings. We conclude with an application to molecular biology. The variety of examples presented here does not exhaust the range of possible applications of the Chen-Stein method. more

325 citations

01 Jan 1976-
Abstract: Definitions and basic properties.- Some miscellaneous results.- Characterization and convergence of non-atomic random measures.- Limit theorems.- Estimation of random variables.- Linear estimation of random variables in stationary doubly stochastic Poisson sequences.- Estimation of second order properties of stationary doubly stochastic Poisson sequences. more

273 citations

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No. of papers in the topic in previous years

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Topic's top 5 most impactful authors

Federico Polito

19 papers, 316 citations

Luisa Beghin

14 papers, 383 citations

Enrico Scalas

13 papers, 318 citations

Nikolai Leonenko

11 papers, 235 citations

Roberto Garra

8 papers, 72 citations