Alexander Bulinski, Alexey Shashkin
Published 2006-08-10Version 1
A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Cs\"{o}rg\H{o} and R\'{e}v\'{e}sz applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed random variables, with the estimate of the convergence rate in the CLT for random fields under consideration.
Comments: Published at http://dx.doi.org/10.1214/074921706000000167 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: IMS Lecture Notes--Monograph Series 2006, Vol. 48, 128-143
A strong invariance principle for associated random fields
Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus
A strong invariance principle for nonconventional sums
![QR code for arXiv:math/0608237 [math.PR]](http://oss.arxitics.com/images/favicon.svg)