scholarly journals Stein’s method for invariant measures of diffusions via Malliavin calculus

2012 ◽  
Vol 122 (4) ◽  
pp. 1627-1651 ◽  
Author(s):  
Seiichiro Kusuoka ◽  
Ciprian A. Tudor
Keyword(s):  
Malliavin Calculus ◽  
Invariant Measures ◽  
Stein’S Method ◽  
Stein's Method

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.

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