scholarly journals Moments of k-hop counts in the random-connection model

2019 ◽  
Vol 56 (4) ◽  
pp. 1106-1121
Author(s):  
Nicolas Privault
Keyword(s):  
Point Process ◽  
Stochastic Integrals ◽  
Model Based ◽  
Random Connection Model

AbstractWe derive moment identities for the stochastic integrals of multiparameter processes in a random-connection model based on a point process admitting a Papangelou intensity. The identities are written using sums over partitions, and they reduce to sums over non-flat partition diagrams if the multiparameter processes vanish on diagonals. As an application, we obtain general identities for the moments of k-hop counts in the random-connection model, which simplify the derivations available in the literature.

scholarly journals On the Ornstein–Zernike equation for stationary cluster processes and the random connection model

2017 ◽  
Vol 49 (4) ◽  
pp. 1260-1287 ◽  
Author(s):  
Günter Last ◽  
Sebastian Ziesche
Keyword(s):  
Point Process ◽  
Cluster Model ◽  
Combinatorial Properties ◽  
Palm Calculus ◽  
Fourier Theory ◽  
Associated Pair ◽  
Special Case ◽  
Random Connection Model ◽  
Palm Probabilities ◽  
Cluster Processes

Abstract In the first part of this paper we consider a general stationary subcritical cluster model in ℝd. The associated pair-connectedness function can be defined in terms of two-point Palm probabilities of the underlying point process. Using Palm calculus and Fourier theory we solve the Ornstein–Zernike equation (OZE) under quite general distributional assumptions. In the second part of the paper we discuss the analytic and combinatorial properties of the OZE solution in the special case of a Poisson-driven random connection model.

Second-order approximation to the characteristic function of certain point-process integrals

1987 ◽  
Vol 19 (3) ◽  
pp. 546-559 ◽  
Author(s):  
Steven P. Ellis
Keyword(s):  
Characteristic Function ◽  
Point Process ◽  
Order Approximation ◽  
Poisson Approximation ◽  
Characteristic Functions ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Kernel Estimates ◽  
Spatial Point ◽  
Better Than

A general way to look at kernel estimates of densities is to regard them as stochastic integrals with respect to a spatial point process. Under regularity conditions these behave asymptotically as if the point process were Poisson. However, this Poisson approximation may not work well if the data exhibits a lot of clustering. In this paper a more refined approximation to the characteristic functions of the integrals is developed. For clustered data, a ‘Gauss–Poisson’ approximation works better than the Poisson.

scholarly journals Minimax regression estimation for Poisson coprocess

2017 ◽  
Vol 21 ◽  
pp. 138-158
Author(s):  
Benoît Cadre ◽  
Nicolas Klutchnikoff ◽  
Gaspar Massiot
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Regression Function ◽  
Stochastic Integrals ◽  
Regression Estimation ◽  
Chaos Expansion ◽  
Adaptive Procedure ◽  
Multiple Stochastic Integrals ◽  
Asymptotic Minimax ◽  
Semiparametric Estimate

For a Poisson point process X, Itô’s famous chaos expansion implies that every square integrable regression function r with covariate X can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where r can be decomposed as a sum of δ chaos. In the spirit of Cadre and Truquet [ESAIM: PS 19 (2015) 251–267], we introduce a semiparametric estimate of r based on i.i.d. copies of the data. We investigate the asymptotic minimax properties of our estimator when δ is known. We also propose an adaptive procedure when δ is unknown.

scholarly journals A Model Based Poisson Point Process for Downlink Cellular Networks Using Joint Scheduling

2019 ◽  
Vol 107 (4) ◽  
pp. 1717-1725
Author(s):  
Sinh Cong Lam ◽  
Kumbesan Sandrasegaran
Keyword(s):  
Cellular Networks ◽  
Point Process ◽  
Poisson Point Process ◽  
Model Based

Evaluation of Automated ECG Monitoring: Theoretical Model Based upon Point Process Techniques

1977 ◽  
Vol 3 (4) ◽  
pp. 283-290
Author(s):  
L.Julian Haywood ◽  
Vrudhula K. Murthy ◽  
George A. Harvey
Keyword(s):  
Theoretical Model ◽  
Point Process ◽  
Ecg Monitoring ◽  
Model Based

Second-order approximation to the characteristic function of certain point-process integrals

1987 ◽  
Vol 19 (03) ◽  
pp. 546-559
Author(s):  
Steven P. Ellis
Keyword(s):  
Characteristic Function ◽  
Point Process ◽  
Order Approximation ◽  
Poisson Approximation ◽  
Characteristic Functions ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Kernel Estimates ◽  
Spatial Point ◽  
Better Than

A general way to look at kernel estimates of densities is to regard them as stochastic integrals with respect to a spatial point process. Under regularity conditions these behave asymptotically as if the point process were Poisson. However, this Poisson approximation may not work well if the data exhibits a lot of clustering. In this paper a more refined approximation to the characteristic functions of the integrals is developed. For clustered data, a ‘Gauss–Poisson’ approximation works better than the Poisson.

Bivariate random closed sets and nerve fibre degeneration

1995 ◽  
Vol 27 (02) ◽  
pp. 293-305 ◽  
Author(s):  
Guillermo Ayala ◽  
Amelia Simó
Keyword(s):  
Nerve Fibre ◽  
Point Process ◽  
Cross Section ◽  
Vertical Cross Section ◽  
Random Set ◽  
Closed Sets ◽  
Model Based ◽  
Random Closed Sets ◽  
Gibbs Point Process ◽  
Two Phases

A biphase image, representing the normal and degenerated fibres in a vertical cross-section of a nerve, is considered. A random set model based on a Gibbs point process is proposed for the union of the two phases. A kind of independence between the degeneration process and the original fibres is defined and tested.

scholarly journals A point process model-based framework reveals reinforcement mechanisms in striatum during high frequency STN DBS

2012 ◽  
Author(s):  
Sabato Santaniello ◽  
John T. Gale ◽  
Erwin B. Montgomery ◽  
Sridevi V. Sarma
Keyword(s):  
Point Process ◽  
High Frequency ◽  
Process Model ◽  
Point Process Model ◽  
Model Based ◽  
Stn Dbs
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