On the characterization of point processes with the order statistic property without the moment condition

1982 ◽  
Vol 19 (1) ◽  
pp. 39-51 ◽  
Author(s):  
Prem S. Puri
Keyword(s):  
Order Statistic ◽  
Point Processes ◽  
Poisson Processes ◽  
Scale Transformation ◽  
Moment Condition ◽  
The Moment ◽  
First Moment ◽  
Multivariate Point ◽  
Multivariate Point Processes

The paper characterizes point processes with the order statistic property without the unnecessary condition of finiteness of the first moment of the process, a condition imposed by previous researchers. It shows that the class of these processes is composed only of mixed Poisson processes up to a time-scale transformation and of the mixed sample processes. It also introduces a multivariate analog of the order statistic property and characterizes completely the class of multivariate point processes with this property.

On the characterization of point processes with the order statistic property without the moment condition

1982 ◽  
Vol 19 (01) ◽  
pp. 39-51 ◽  
Author(s):  
Prem S. Puri
Keyword(s):  
Order Statistic ◽  
Point Processes ◽  
Poisson Processes ◽  
Scale Transformation ◽  
Moment Condition ◽  
The Moment ◽  
First Moment ◽  
Multivariate Point ◽  
Multivariate Point Processes

The paper characterizes point processes with the order statistic property without the unnecessary condition of finiteness of the first moment of the process, a condition imposed by previous researchers. It shows that the class of these processes is composed only of mixed Poisson processes up to a time-scale transformation and of the mixed sample processes. It also introduces a multivariate analog of the order statistic property and characterizes completely the class of multivariate point processes with this property.

A characterization of order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously

1985 ◽  
Vol 22 (02) ◽  
pp. 314-323
Author(s):  
A. Deffner ◽  
E. Haeusler
Keyword(s):  
Order Statistic ◽  
Real Line ◽  
Time Scale ◽  
Point Processes ◽  
Present Note ◽  
Poisson Processes ◽  
Scale Transformation ◽  
The Real ◽  
Mixed Sample

The results of Nawrotzki (1962), Feigin (1979) and Puri (1982) show that the class of all point processes (on the real line) with the order statistic property consists of all mixed Poisson processes up to a time-scale transformation, and of all mixed sample processes. The present note characterizes those order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously.

A characterization of order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously

1985 ◽  
Vol 22 (2) ◽  
pp. 314-323 ◽  
Author(s):  
A. Deffner ◽  
E. Haeusler
Keyword(s):  
Order Statistic ◽  
Real Line ◽  
Time Scale ◽  
Point Processes ◽  
Present Note ◽  
Poisson Processes ◽  
Scale Transformation ◽  
The Real ◽  
Mixed Sample

The results of Nawrotzki (1962), Feigin (1979) and Puri (1982) show that the class of all point processes (on the real line) with the order statistic property consists of all mixed Poisson processes up to a time-scale transformation, and of all mixed sample processes. The present note characterizes those order statistic point processes that are mixed Poisson processes and mixed sample processes simultaneously.

Orderliness, intensities and Palm-Khinchin equations for multivariate point processes

1975 ◽  
Vol 12 (2) ◽  
pp. 383-389 ◽  
Author(s):  
D. J. Daley ◽  
R. K. Milne
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Multivariate Point ◽  
Multivariate Point Processes

Simple definitions and derivations of elementary properties are given for the various intensities and Palm-Khinchin functions associated with a multivariate point process.

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