A Point Process with Second Order MARKOV Dependent Intervals

1981 ◽  
Vol 103 (1) ◽  
pp. 155-163
Author(s):  
F. S. Chong
Keyword(s):  
Point Process ◽  
Second Order

Dependent thinning of point processes

1980 ◽  
Vol 17 (04) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Dependent thinning of point processes

1980 ◽  
Vol 17 (4) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

An identification problem in almost and asymptotically almost periodically correlated processes

1982 ◽  
Vol 19 (2) ◽  
pp. 456-462 ◽  
Author(s):  
Y. Isokawa
Keyword(s):  
Random Process ◽  
Point Process ◽  
Identification Problem ◽  
Second Order ◽  
Linear Filter ◽  
Minimum Phase ◽  
Periodically Correlated Processes ◽  
Time Invariant

Consider a unknown realizable time-invariant linear filter driven by a point process. We are interested in the identification of this system, observing only the output random process. If the process is almost periodically correlated but not periodically correlated, we can identify the filter, using the second-order non-stationary spectrum of the process. We do not require the assumption that the filter is minimum phase.

θ-stationary point processes and their second-order analysis

1981 ◽  
Vol 18 (04) ◽  
pp. 864-878
Author(s):  
Karen Byth
Keyword(s):  
Point Process ◽  
Spatial Patterns ◽  
Stationary Point ◽  
Point Processes ◽  
Simulated Data ◽  
Second Order ◽  
Stationary Processes ◽  
Order Analysis ◽  
Stationary Point Processes ◽  
Point Of Reference

The concept of θ-stationarity for a simple second-order point process in R2 is introduced. This concept is closely related to that of isotropy. Some θ-stationary processes are defined. Techniques are given for simulating realisations of these processes. The second-order analysis of these processes which have an obvious point of reference or origin is considered. Methods are suggested for modelling spatial patterns which are realisations of such processes. These methods are illustrated using simulated data. The ideas are extended to multitype point processes.

θ-stationary point processes and their second-order analysis

1981 ◽  
Vol 18 (4) ◽  
pp. 864-878 ◽  
Author(s):  
Karen Byth
Keyword(s):  
Point Process ◽  
Spatial Patterns ◽  
Stationary Point ◽  
Point Processes ◽  
Simulated Data ◽  
Second Order ◽  
Stationary Processes ◽  
Order Analysis ◽  
Stationary Point Processes ◽  
Point Of Reference

The concept of θ-stationarity for a simple second-order point process in R2 is introduced. This concept is closely related to that of isotropy. Some θ-stationary processes are defined. Techniques are given for simulating realisations of these processes. The second-order analysis of these processes which have an obvious point of reference or origin is considered. Methods are suggested for modelling spatial patterns which are realisations of such processes. These methods are illustrated using simulated data. The ideas are extended to multitype point processes.

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.

A Versatile Packet Arrival Process and Its Second Order Properties

1993 ◽  
Vol 7 (4) ◽  
pp. 495-513 ◽  
Author(s):  
Teunis J. Ott
Keyword(s):  
Point Process ◽  
Generating Function ◽  
Discrete Time ◽  
Branching Process ◽  
Second Order ◽  
Arrival Process ◽  
Multitype Branching Process ◽  
Infected People ◽  
Index Of Dispersion ◽  
Packet Arrival

In this paper we describe a class of discrete time processes that can be used to model packet arrival streams in packetized communication. Mathematically, (K(t)) can be seen as a discrete time self-exciting point process, as a multitype branching process, or as an epidemic with immigration of infected people. The purpose of this paper is to show that this class of models simultaneously is quite useful and analytically more tractable than is obvious at first glance. It is shown that certain probabilities can reliably be computed using generating function methods, and expressions are given for the second order properties and for the asymptotic index of dispersion.

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