Some limit theorems for the empirical process indexed by functions

1987 ◽  
Vol 74 (1) ◽  
pp. 71-90 ◽  
Author(s):  
J. E. Yukich
2013 ◽  
Vol 45 (2) ◽  
pp. 379-397
Author(s):  
Shui Feng ◽  
Jie Xiong

The asymptotic behavior is studied for an interacting particle system that involves independent motion and random sampling. For a fixed sampling rate, the empirical process of the particle system converges to the Fleming-Viot process when the number of particles approaches ∞. If the sampling rate approaches 0 as the number of particles becomes large, the corresponding empirical process will converge to the deterministic flow of the motion. In the main results of this paper, we study the corresponding central limit theorems and large deviations. Both the Gaussian limits and the large deviations depend on the sampling scales explicitly.


2013 ◽  
Vol 45 (02) ◽  
pp. 379-397
Author(s):  
Shui Feng ◽  
Jie Xiong

The asymptotic behavior is studied for an interacting particle system that involves independent motion and random sampling. For a fixed sampling rate, the empirical process of the particle system converges to the Fleming-Viot process when the number of particles approaches∞. If the sampling rate approaches 0 as the number of particles becomes large, the corresponding empirical process will converge to the deterministic flow of the motion. In the main results of this paper, we study the corresponding central limit theorems and large deviations. Both the Gaussian limits and the large deviations depend on the sampling scales explicitly.


Author(s):  
J.A. Eades ◽  
E. Grünbaum

In the last decade and a half, thin film research, particularly research into problems associated with epitaxy, has developed from a simple empirical process of determining the conditions for epitaxy into a complex analytical and experimental study of the nucleation and growth process on the one hand and a technology of very great importance on the other. During this period the thin films group of the University of Chile has studied the epitaxy of metals on metal and insulating substrates. The development of the group, one of the first research groups in physics to be established in the country, has parallelled the increasing complexity of the field.The elaborate techniques and equipment now needed for research into thin films may be illustrated by considering the plant and facilities of this group as characteristic of a good system for the controlled deposition and study of thin films.


1998 ◽  
Vol 77 (5) ◽  
pp. 1353-1356
Author(s):  
Rosario N. Mantegna, H. Eugene Stanley

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 1473-1503 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu

Sign in / Sign up

Export Citation Format

Share Document