Generalized Shock Models Based on a Cluster Point Process

2006 ◽  
Vol 55 (3) ◽  
pp. 542-550 ◽  
Author(s):  
J.-M. Bai ◽  
Z.-H. Li ◽  
X.-B. Kong
Keyword(s):  
Point Process ◽  
Cluster Point ◽  
Cluster Point Process ◽  
Shock Models

Modeling and Analysis of NOMA Enabled CRAN with Cluster Point Process

2017 ◽  
Author(s):  
Francisco J. Martin-Vega ◽  
Yuanwei Liu ◽  
Gerardo Gomez ◽  
Mari Carmen Aguayo-Torres ◽  
Maged Elkashlan
Keyword(s):  
Point Process ◽  
Cluster Point ◽  
Modeling And Analysis ◽  
Cluster Point Process

Interacting cluster point process model for epidermal nerve fibers

2020 ◽  
Vol 35 ◽  
pp. 100414
Author(s):  
Nancy L. Garcia ◽  
Peter Guttorp ◽  
Guilherme Ludwig
Keyword(s):  
Point Process ◽  
Process Model ◽  
Nerve Fibers ◽  
Cluster Point ◽  
Point Process Model ◽  
Cluster Point Process

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

Limit theorems for jump shock models

1989 ◽  
Vol 26 (4) ◽  
pp. 793-806 ◽  
Author(s):  
Keigo Yamada
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Limit Theorems ◽  
Stable Process ◽  
Deterministic Process ◽  
Shock Process ◽  
Shock Models

We consider an additive shock process where shocks occur according to a Poisson point process and they are accumulated in an appropriate way to the damage. It is shown that suitably normalized shock processes converge weakly to a process which is represented as a sum of a stable process and a deterministic process.

A two-dimensional ‘immigration–branching' model with application to earthquake occurrence times and energies

1977 ◽  
Vol 14 (03) ◽  
pp. 464-474
Author(s):  
C. D. Lai
Keyword(s):  
Point Process ◽  
Two Dimensional ◽  
Earthquake Occurrence ◽  
Generating Functional ◽  
Cluster Centre ◽  
Branching Model ◽  
Cluster Point Process ◽  
Moment Measures ◽  
Poisson Cluster ◽  
Occurrence Times

A two-dimensional Poisson cluster point process is formulated by the use of a probability generating functional. Moment measures of both the cluster centre and member processes are discussed. An example is provided, and the magnitude frequency law is proved in this case.

Limit theorems for jump shock models

1989 ◽  
Vol 26 (04) ◽  
pp. 793-806
Author(s):  
Keigo Yamada
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Limit Theorems ◽  
Stable Process ◽  
Deterministic Process ◽  
Shock Process ◽  
Shock Models

We consider an additive shock process where shocks occur according to a Poisson point process and they are accumulated in an appropriate way to the damage. It is shown that suitably normalized shock processes converge weakly to a process which is represented as a sum of a stable process and a deterministic process.

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