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Poisson point and Poisson processes
2017This chapter starts with a general description of Poisson point processes. These processes are defined from four natural axioms describing the spatial distribution of so-called Poisson points scattered homogeneously in a random manner across the d-dimensional Euclidean space.
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Poisson branching point processes
Journal of Mathematical Physics, 1984We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage.
Kuniaki Matsuo +2 more
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On the distribution of points in a poisson dirichlet process
Journal of Applied Probability, 1988A probability density function important in the Poisson Dirichlet process of population genetics is studied. An accurate computational algorithm is given for this density and for the marginal distributions of the points in the Poisson Dirichlet process. The distribution of the maximal point of the process is tabulated.
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2014
Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.
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Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.
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2015
Throughout this note we will use the following notations. An interval of the type [l, r), \(-\infty < l < r \le \infty \) is called a time interval and is denoted by \(T, T_1, T_2, \ldots \). T is regarded as a measurable space associated with the topological \(\sigma \)-algebra on \(\mathscr {T}\) on T.
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Throughout this note we will use the following notations. An interval of the type [l, r), \(-\infty < l < r \le \infty \) is called a time interval and is denoted by \(T, T_1, T_2, \ldots \). T is regarded as a measurable space associated with the topological \(\sigma \)-algebra on \(\mathscr {T}\) on T.
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Bayesian Analysis of a Poisson Process with a Change-Point
Biometrika, 1986SUMMARY A Bayesian approach to estimation and hypothesis testing for a Poisson process with a change-point is developed, and an example given.
A. E. RAFTERY, V. E. AKMAN
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Point processes subordinated to compound Poisson processes
Theory of Probability and Mathematical Statistics, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kobylych, K. V., Sakhno, L. M.
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Scanning Points in a Poisson Process
2001Let Y t (w) denote the number of points (X’s) in the interval {t, t + w). The scan statistic \( {S_w} = \mathop {\max }\limits_{0 < t < T - w} \;\{ {Y_t}(w)\}\), denotes the largest number of points to be found in any subinterval of [0, T) of length w. Let X (1) ≤ X (2) ≤ ...,denote the ordered values of the X’s.
Joseph Glaz +2 more
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Splash of Solid Particles as a Stochastic Point Process
Journal of Geophysical Research: Earth Surface, 2019A splash experiment was carried out on a model soil–glass beads with a diameter of 425–600 μm using high‐speed cameras and sticky paper. Two different types of particles were involved in the process: droplets of water and glass beads.
A. Sochan +7 more
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Poisson point processes with exclusion
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1978We give the definition of Poisson point processes with exclusion by their local conditional distributions, treat the existence and uniqueness problem and their applications in percolation theory.
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