Pattern theorems, ratio limit theorems and Gumbel maximal clusters for random fields

The Erwin Schrr Odinger International Institute for Mathematical Physics Martingale-diierence Random Fields Limit Theorems and Some Applications Martingale-diierence Random Fields. Limit Theorems and Some Applications

Some convergence results on quadratic forms for random fields and application to empirical covariances

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our limit theorems and those of Ginovian (1999) to obtain the asymptotic behavior of the empirical covariances of Gaussian fields, which is a particular example o...

The Concept of Sub-independence and Its Application in Statistics and Probabilities

 Many Limit Theorems, Convergence Theorems and Characterization Theorems in Probability and Statistics, in particular those related to normal distribution , are based on the assumption of independence of two or more random variables. However, the full power of independence is not used in the proofs of these Theorems, since it is the distribution of summation of the random variables whic...

Large deviations of combinatorial distributions II: Local limit theorems

This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we a...

Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields.

Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building block...