scholarly journals The random connection model and functions of edge-marked Poisson processes: Second order properties and normal approximation

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Günter Last ◽  
Franz Nestmann ◽  
Matthias Schulte
Keyword(s):  
Normal Approximation ◽  
Second Order ◽  
Poisson Processes ◽  
Random Connection Model

Random Johnson-Mehl tessellations

1992 ◽  
Vol 24 (04) ◽  
pp. 814-844 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Euclidean Space ◽  
Second Order ◽  
Poisson Processes ◽  
Dimensional Euclidean Space ◽  
Inhomogeneous Poisson Processes

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

Random Johnson-Mehl tessellations

1992 ◽  
Vol 24 (4) ◽  
pp. 814-844 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Euclidean Space ◽  
Second Order ◽  
Poisson Processes ◽  
Dimensional Euclidean Space ◽  
Inhomogeneous Poisson Processes

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

scholarly journals Normal approximation for weighted sums under a second-order correlation condition

2020 ◽  
Vol 48 (3) ◽  
pp. 1202-1219
Author(s):  
S. G. Bobkov ◽  
G. P. Chistyakov ◽  
F. Götze
Keyword(s):  
Normal Approximation ◽  
Second Order ◽  
Weighted Sums

Weak homogenization of point processes by space deformations

2000 ◽  
Vol 32 (4) ◽  
pp. 948-959 ◽  
Author(s):  
R. Senoussi ◽  
J. Chadœuf ◽  
D. Allard
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Second Order ◽  
Poisson Processes ◽  
Borel Set ◽  
First Order ◽  
Stationary Point Process

We study the transformation of a non-stationary point process ξ on ℝn into a weakly stationary point process ͂ξ, with ͂ξ(B) = ξ(Φ-1(B)), where B is a Borel set, via a deformation Φ of the space ℝn. When the second-order measure is regular, Φ is uniquely determined by the homogenization equations of the second-order measure. In contrast, the first-order homogenization transformation is not unique. Several examples of point processes and transformations are investigated with a particular interest to Poisson processes.

scholarly journals The Berry-Esseen bound for the Poisson shot-noise

1987 ◽  
Vol 19 (2) ◽  
pp. 512-514 ◽  
Author(s):  
John A. Lane
Keyword(s):  
Statistical Analysis ◽  
Shot Noise ◽  
Point Processes ◽  
Normal Approximation ◽  
Poisson Processes ◽  
Cluster Point ◽  
Special Cases ◽  
Poisson Shot Noise

This note provides a useful extension of the Berry–Esseen bound on the error in the normal approximation for shot-noise. The special cases treated are of particular interest in the statistical analysis of Poisson processes and cluster point processes.

scholarly journals The Berry-Esseen bound for the Poisson shot-noise

1987 ◽  
Vol 19 (02) ◽  
pp. 512-514 ◽  
Author(s):  
John A. Lane
Keyword(s):  
Statistical Analysis ◽  
Shot Noise ◽  
Point Processes ◽  
Normal Approximation ◽  
Poisson Processes ◽  
Cluster Point ◽  
Special Cases ◽  
Poisson Shot Noise

This note provides a useful extension of the Berry–Esseen bound on the error in the normal approximation for shot-noise. The special cases treated are of particular interest in the statistical analysis of Poisson processes and cluster point processes.

Spectral modelling of homogeneous non-isotropic turbulence

1981 ◽  
Vol 104 ◽  
pp. 247-262 ◽  
Author(s):  
C. Cambon ◽  
D. Jeandel ◽  
J. Mathieu
Keyword(s):  
Fourier Transform ◽  
Spherical Shell ◽  
Velocity Gradient ◽  
Numerical Solutions ◽  
Isotropic Turbulence ◽  
Normal Approximation ◽  
Second Order ◽  
Mean Velocity ◽  
The Fourier Transform

The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.

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