Corrigendum to: Exponential Moments and Piecewise Thinning for the Bessel Point Process

2021 ◽  
Author(s):  
Christophe Charlier
Keyword(s):  
Point Process ◽  
Exponential Moments

On the moments of a self-correcting process

1984 ◽  
Vol 21 (2) ◽  
pp. 335-342 ◽  
Author(s):  
D. Vere-Jones ◽  
Y. Ogata
Keyword(s):  
Markov Chain ◽  
Point Process ◽  
Conditional Intensity ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Exponential Moments ◽  
Image Position

The existence of ordinary and exponential moments of a point process with conditional intensity of the formis deduced from a Markov chain representation fort – ρN(t). These results form an application of recent theorems of Tweedie (1983a, b) and are used to obtain laws of large numbers for a range of functionals of the process.

On the moments of a self-correcting process

1984 ◽  
Vol 21 (02) ◽  
pp. 335-342 ◽  
Author(s):  
D. Vere-Jones ◽  
Y. Ogata
Keyword(s):  
Markov Chain ◽  
Point Process ◽  
Conditional Intensity ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Exponential Moments ◽  
Image Position

The existence of ordinary and exponential moments of a point process with conditional intensity of the form is deduced from a Markov chain representation for t – ρN(t). These results form an application of recent theorems of Tweedie (1983a, b) and are used to obtain laws of large numbers for a range of functionals of the process.

scholarly journals Exponential Moments and Piecewise Thinning for the Bessel Point Process

2020 ◽  
Author(s):  
Christophe Charlier
Keyword(s):  
Point Process ◽  
Central Limit ◽  
Limit Theorems ◽  
Counting Function ◽  
Direct Consequence ◽  
Central Limit Theorems ◽  
Exponential Moment ◽  
Piecewise Constant ◽  
Global Rigidity ◽  
Exponential Moments

Abstract We obtain exponential moment asymptotics for the Bessel point process. As a direct consequence, we improve on the asymptotics for the expectation and variance of the associated counting function and establish several central limit theorems. We show that exponential moment asymptotics can also be interpreted as large gap asymptotics, in the case where we apply the operation of a piecewise constant thinning on several consecutive intervals. We believe our results also provide important estimates for later studies of the global rigidity of the Bessel point process.

Habitat use of toothed whales in a marine protected area based on point process models

2019 ◽  
Vol 609 ◽  
pp. 239-256 ◽  
Author(s):  
TL Silva ◽  
G Fay ◽  
TA Mooney ◽  
J Robbins ◽  
MT Weinrich ◽  
...  
Keyword(s):  
Habitat Use ◽  
Point Process ◽  
Protected Area ◽  
Marine Protected Area ◽  
Process Models ◽  
Point Process Models

On the generation and origin of I/f noise

1999 ◽  
Vol 4 ◽  
pp. 87-96 ◽  
Author(s):  
B. Kaulakys ◽  
T. Meškauskas
Keyword(s):  
Point Process ◽  
Solvable Model ◽  
Autoregressive Process ◽  
Wide Range ◽  
Occurrence Times

Simple analytically solvable model exhibiting 1/f spectrum in any desirably wide range of frequency is analysed. The model consists of pulses (point process) whose interevent times obey an autoregressive process with small damping. Analysis and generalizations of the model indicate to the possible origin of 1/f noise, i.e. random increments between the occurrence times of particles or pulses resulting in the clustering of the pulses.

Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

2020 ◽  
Vol 2020 (14) ◽  
pp. 305-1-305-6
Author(s):  
Tianyu Li ◽  
Camilo G. Aguilar ◽  
Ronald F. Agyei ◽  
Imad A. Hanhan ◽  
Michael D. Sangid ◽  
...  
Keyword(s):  
Composite Material ◽  
Point Process ◽  
Marked Point ◽  
Experimental Results ◽  
Marked Point Process ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Proposed Model ◽  
Cylinder Model ◽  
Reinforced Composite Material

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

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