scholarly journals A strong invariance principle for negatively associated random fields

2011 ◽  
Vol 61 (1) ◽  
pp. 27-40 ◽  
Author(s):  
Guang-hui Cai
Keyword(s):  
Invariance Principle ◽  
Random Fields ◽  
Negatively Associated ◽  
Strong Invariance ◽  
Strong Invariance Principle

scholarly journals Rates in the strong invariance principle for ergodic automorphisms of the torus

2014 ◽  
Vol 14 (02) ◽  
pp. 1350021
Author(s):  
Jérôme Dedecker ◽  
Florence Merlevède ◽  
Françoise Pène
Keyword(s):  
Invariance Principle ◽  
Fourier Coefficients ◽  
Rates Of Convergence ◽  
Partial Sums ◽  
Dimensional Torus ◽  
Strong Invariance ◽  
Ergodic Automorphism ◽  
Strong Invariance Principle ◽  
Natural Way

Let T be an ergodic automorphism of the d-dimensional torus 𝕋d. In the spirit of Le Borgne, we give conditions on the Fourier coefficients of a function f from 𝕋d to ℝ under which the partial sums f ◦ T + f ◦ T2 + ⋯ + f ◦ Tn satisfy a strong invariance principle. Next, reinforcing the condition on the Fourier coefficients in a natural way, we obtain explicit rates of convergence in the strong invariance principle, up to n1/4 log n.

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