Central Limit Theorems for Weakly Dependent Random Fields

Авторы: Bulinski A., Spodarev E.
Сборник: Stochastic Geometry, Spatial Statistics and Random Fields
Серия: Lecture Notes in Mathematics
Том: 2068
Год издания: 2013
Издательство: SPRINGER-VERLAG BERLIN
Местоположение издательства: HEIDELBERGER PLATZ 3, BERLIN, GERMANY,D-14197
Первая страница: 336
Последняя страница: 383
DOI: 10.1007/978-3-642-33305-7
Аннотация: This chapter is a primer on the limit theorems for dependent random fields. First, dependence concepts such as mixing, association and their generalizations are introduced. Then, moment inequalities for sums of dependent random variables are stated which yield e.g. the asymptotic behaviour of the variance of these sums which is essential for the proof of limit theorems. Finally, central limit theorems for dependent random fields are given. Applications to excursion sets of random fields and Newman’s conjecture in the absence of finite susceptibility are discussed as well.
Добавил в систему: Булинский Александр Вадимович

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