Uniform convergence in probability of wavelet expansions of random processes from L 2(Ω)

2008 ◽  
Vol 16 (4) ◽  
Author(s):  
Yu. V. Kozachenko ◽  
O. V. Polosmak
Keyword(s):  
Uniform Convergence ◽  
Random Processes ◽  
Convergence In Probability ◽  
Wavelet Expansions

On uniform convergence of wavelet expansions of ϕ-sub-Gaussian random processes

2006 ◽  
Vol 14 (3) ◽  
pp. 209-232 ◽  
Author(s):  
Yu. V. Kozachenko ◽  
M. M. Perestyuk ◽  
O. I. Vasylyk
Keyword(s):  
Uniform Convergence ◽  
Random Processes ◽  
Wavelet Expansions

scholarly journals Uniform Convergence of Wavelet Expansions of Gaussian Random Processes

2011 ◽  
Vol 29 (2) ◽  
pp. 169-184 ◽  
Author(s):  
Yuriy Kozachenko ◽  
Andriy Olenko ◽  
Olga Polosmak
Keyword(s):  
Uniform Convergence ◽  
Random Processes ◽  
Wavelet Expansions

scholarly journals Generic Uniform Convergence

1992 ◽  
Vol 8 (2) ◽  
pp. 241-257 ◽  
Author(s):  
Donald W.K. Andrews
Keyword(s):  
Uniform Convergence ◽  
Asymptotic Properties ◽  
Convergence In Probability ◽  
Test Statistics ◽  
Parameter Spaces ◽  
Totally Bounded ◽  
Convergence Results ◽  
Large Numbers ◽  
Uniform Law ◽  
Convergence Almost Surely

This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics.The results given here have the following attributes, (1) they extendresults of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for i.i.d. contexts, but which apply in some dependent nonidentically distributed contexts as well, and (4) they incorporate and extend themain results in the literature in a parsimonious fashion.

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