Limit Theorems for Associated Random Fields and Related Systems
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Focusing on the asymptotic properties of wide classes of stochastic systems as the arise in mathematical statistics, percolation theory, statistical physics and reliability theory, Bulinski and Shashkin (both mathematics, Moscow State U.) provide detailed proofs as well as auxiliary results. They address positive and negative associations introduced by pioneering papers but also new and more general dependence conditions as well as examples of Markov processes. They cover random systems with covariance inequalities, moment and maximal inequalities, the central limit theorem, the "almost sure" ...
Focusing on the asymptotic properties of wide classes of stochastic systems as the arise in mathematical statistics, percolation theory, statistical physics and reliability theory, Bulinski and Shashkin (both mathematics, Moscow State U.) provide detailed proofs as well as auxiliary results. They address positive and negative associations introduced by pioneering papers but also new and more general dependence conditions as well as examples of Markov processes. They cover random systems with covariance inequalities, moment and maximal inequalities, the central limit theorem, the "almost sure" convergence, invariance principles, the law of the iterated logarithm, statistical applications, and integral functionals. The bibliography is very comprehensive. His book would work well for researchers as well as graduate students.
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