Central limit theorems for long range dependent spatial linear processes

Central Limit Theorems for Arrays of Decimated Linear Processes

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the s...

Central Limit Theorems For Dependent, Heterogeneous Processes With Trending Moments

Central Limit Theorems For Superlinear Processes

The Central Limit Theorem is studied for stationary sequences that are sums of countable collections of linear processes. Two sets of sufficient conditions are obtained. One restricts only the coefficients and is shown to be best possible among such conditions. The other involves an interplay between the coefficients and the distribution functions of the innovations and is shown to be necessary...

Central Limit Theorems for Dependent Random Variables

1. Limiting distributions of sums of 'small' independent random variables have been extensively studied and there is a satisfactory general theory of the subject (see e.g. the monograph of B.V. Gnedenko and A.N. Kolmogorov [2]). These results are conveniently formulated for double arrays Xn k (k = 1, . . . , kn ; n = 1, 2, . . . ) of random variables where the Xn k (k = 1, . . . , kn), the rand...

Central limit theorems in linear dynamics

Given a bounded operator T on a Banach space X, we study the existence of a probability measure μ on X such that, for many functions f : X → K, the sequence (f + · · ·+ f ◦ T)/ √ n converges in distribution to a Gaussian random variable.