Alexey Shashkin

Limit theorems for associated random fields and related systems

Random Systems with Covariance Inequalities Moment and Maximal Inequalities Central Limit Theorem Almost Sure Convergence Invariance Principles Law of the Iterated Logarithm Statistical Applications Integral Functionals.

Strong invariance principle for dependent random fields

A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative associ- ation. We use the approach of Csorgýo and Revesz 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 mul- tiindexed random variables, with the estimate of the convergence rate in the CLT for random fields under consideration.

A Berry – Esseen Type Estimate for Dependent Systems on Transitive Graphs

Dependent random systems indexed by transitive graphs are studied. The dependence structure generalizes the ideas of positive and negative association. For such random systems the CLT is proved and the rate of convergence is established.