Alexander Bulinski

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.

Normal approximation for quasi-associated random fields

For quasi-associated random fields (comprising negatively and positively dependent fields) on we use Steins method to establish the rate of normal approximation for partial sums taken over arbitrary finite subsets of .

Central limit theorems for the excursion set volumes of weakly dependent random fields

The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on

Invariance principle for associated random fields

\mathbb{R}^d

Strong invariance principle for dependent random fields

are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed.

Central Limit Theorem for Random Fields and Applications

In 1984, C. M. Newman posed the problem of proving the invariance principle in distribution for associated random fields (i. e., fields satisfying the so-called FKG-inequalities)X={Xj, j∈Zd} when d≥3. The solution of this problem for wide-sense stationary associated random fields is obtained here under slightly more restrictive conditions than those used by C. M. Newman and A. L. Wright for the strictly stationary case where d=1 and d=2.

Conditional Central Limit Theorem

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.

Simulation and Analytical Approach to the Identification of Significant Factors

A new variant of the CLT is established for random fields defined on ℝ d which are strictly stationary, with a finite second moment and weakly dependent (comprising cases of positive or negative association). The summation domains grow in the van Hove sense. At the same time the indices of observations form more and more dense grids in these domains. Thus the effect of combining two scaling procedures is studied. A statistical version of this CLT is also proved. Some stochastic models in radiobiology based on dependent functional subunits are discussed as well.

Central Limit Theorem Related to MDR-Method

The arrays with rows consisting of conditionally independent random variables with respect to certain

Central Limit Theorems for Weakly Dependent Random Fields

\sigma