scholarly journals Poisson process approximation: From Palm theory to Stein’s method

2006 ◽  
pp. 236-244 ◽  
Author(s):  
Louis H. Y. Chen ◽  
Aihua Xia
Keyword(s):  
Poisson Process ◽  
Stein’S Method ◽  
Stein's Method ◽  
Process Approximation

On the rate of Poisson process approximation to a Bernoulli process

1997 ◽  
Vol 34 (4) ◽  
pp. 898-907 ◽  
Author(s):  
Aihua Xia
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Discrete Time ◽  
Wasserstein Distance ◽  
Stein’S Method ◽  
Upper Bounds ◽  
Stein's Method ◽  
Bernoulli Process ◽  
Logarithmic Factor ◽  
Process Approximation

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.

On the rate of Poisson process approximation to a Bernoulli process

1997 ◽  
Vol 34 (04) ◽  
pp. 898-907 ◽  
Author(s):  
Aihua Xia
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Discrete Time ◽  
Wasserstein Distance ◽  
Stein’S Method ◽  
Upper Bounds ◽  
Stein's Method ◽  
Bernoulli Process ◽  
Logarithmic Factor ◽  
Process Approximation

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.

Stein's method and poisson process convergence

1988 ◽  
Vol 25 (A) ◽  
pp. 175-184 ◽  
Author(s):  
A. D. Barbour
Keyword(s):  
Point Processes ◽  
Rates Of Convergence ◽  
Poisson Approximation ◽  
Stein’S Method ◽  
Simple Problem ◽  
Stein's Method ◽  
General Technique ◽  
One Dimensional ◽  
Process Convergence ◽  
Process Approximation

Stein's method of obtaining rates of convergence, well known in normal and Poisson approximation, is considered here in the context of approximation by Poisson point processes, rather than their one-dimensional distributions. A general technique is sketched, whereby the basic ingredients necessary for the application of Stein's method may be derived, and this is applied to a simple problem in Poisson point process approximation.

Stein's method and poisson process convergence

1988 ◽  
Vol 25 (A) ◽  
pp. 175-184 ◽  
Author(s):  
A. D. Barbour
Keyword(s):  
Point Processes ◽  
Rates Of Convergence ◽  
Poisson Approximation ◽  
Stein’S Method ◽  
Simple Problem ◽  
Stein's Method ◽  
General Technique ◽  
One Dimensional ◽  
Process Convergence ◽  
Process Approximation

Stein's method of obtaining rates of convergence, well known in normal and Poisson approximation, is considered here in the context of approximation by Poisson point processes, rather than their one-dimensional distributions. A general technique is sketched, whereby the basic ingredients necessary for the application of Stein's method may be derived, and this is applied to a simple problem in Poisson point process approximation.

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