A strong invariance principle for associated random fields

2005/03/01 by Raluca M. Balan
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Probability and Risk Models #Stochastic processes and financial applications #math.PR #msc:60F17 #msc:60G60 #msc:60K35.

paper · pdf · doi:10.1214/009117904000001071

published as Annals of Probability 2005, Vol. 33, No. 2, 823-840 · Published at http://dx.doi.org/10.1214/009117904000001071 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/03/01 · arxiv created 2005/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we generalize Yu’s [Ann. Probab. 24 (1996) 2079–2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n→∞. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15–37] multi-parameter blocking technique, the Csörgő and Révész [Z. Wahrsch. Verw. Gebiete 31 (1975) 255–260] quantile transform method and the Bulinski [Theory Probab. Appl. 40 (1995) 136–144] rate of convergence in the CLT.

Citations

• Almost sure invariance principles for partial sums of weakly dependent random variables
• Association of Random Variables, with Applications

Related

• On the invariance principle for empirical processes of associated sequences
• A Nonconventional Invariance Principle for Random Fields
• Strong approximations for a class of dependent random variables with semi exponential tails
• A New Condition for the Invariance Principle for Stationary Random Fields
• A simple invariance theorem