In many situations when sequences of random vectors are under consideration, it is of interest to study the asymptotic distribution of their (normalized) sums and to determine the conditions for the limit theorems, such as the Central Limit Theorem (CLT), to hold. In the simplest case when the variables are independent and identically distributed and have finite variance, the CLT is satisfied. Some CLT generalizations with weakened independence assumptions exist as well. For example, the CLT holds for stationary random sequences with strong mixing. However, in many situations when there is dependence, the CLT does not hold.%In particular when we consider stationary sequences of random variables.This happens for stationary random sequences even with the weak mixing condition.In our research we propose a method of random modulation of ergodic stationary random sequences that allows us to prove limit theorems for such sequences without any mixing conditions. These theorems present an opportunity to construct asymptotic confidence intervals for parameters, test parametric and non-parametric hypotheses with the significance level close to the required one and to calculate the approximate power of the test.More general analogs of the CLT are proved and the speed of convergence is estimated for sequences of random vectors in spaces of non-decreasing dimensions.

A discussion of some topics in the theory of large deviations such as moment-generating functions and Chernoff's theorem, and of aspects of estimation and testing in large samples, such as exact slopes of test statistics.

A central limit theorem is given with application to a wide class of processes ((S sub M) = summation from i = 1 to n of (X sub i)) with stationary ergodic increments (X sub i) having zero mean and finite variance and such that lim as N approaches infinity (N sup -1) E (S sup 2, sub n) = (Sigma squared), 0

Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR