Measuring the Dependence between Two Point Processes through Confidence Intervals for the Second Order Distribution.

1987 ◽  
Author(s):  
Hani Doss
Keyword(s):  
Confidence Intervals ◽  
Point Processes ◽  
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.

Some models for multitype spatial point processes, with remarks on analysing multitype patterns

1984 ◽  
Vol 21 (3) ◽  
pp. 575-582 ◽  
Author(s):  
H. W. Lotwick
Keyword(s):  
Point Processes ◽  
Empty Space ◽  
Second Order ◽  
Spatial Point Processes ◽  
Spatial Point ◽  
Methods Of Analysis ◽  
Second Order Methods

Two classes of ergodic stationary multitype spatial point processes are constructed. These processes have the property that interactions between the types exist, but cannot be detected using standard second-order methods of analysis. Simulations indicate that the interactions can, however, be detected by using ‘empty space' techniques.

ESTIMATION AND SIMULATION OF FRACTAL STOCHASTIC POINT PROCESSES

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 183-210 ◽  
Author(s):  
STEVEN B. LOWEN ◽  
MALVIN C. TEICH
Keyword(s):  
Fractal Dimension ◽  
Finite Length ◽  
Point Processes ◽  
Second Order ◽  
Dimension Analysis ◽  
Analytical Properties ◽  
Fractal Dimension Analysis ◽  
Stochastic Point Processes

We investigate the properties of fractal stochastic point processes (FSPPs). First, we define FSPPs and develop several mathematical formulations for these processes, showing that over a broad range of conditions they converge to a particular form of FSPP. We then provide examples of a wide variety of phenomena for which they serve as suitable models. We proceed to examine the analytical properties of two useful fractal dimension estimators for FSPPs, based on the second-order properties of the points. Finally, we simulate several FSPPs, each with three specified values of the fractal dimension. Analysis and simulation reveal that a variety of factors confound the estimate of the fractal dimension, including the finite length of the simulation, structure or type of FSPP employed, and fluctuations inherent in any FSPP. We conclude that for segments of FSPPs with as many as 106 points, the fractal dimension can be estimated only to within ±0.1.

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