Exact rate of convergence for large increments of random fields

Abstract

We invertigate the rate of convergence in strong limit theorems for the maximum increment of a randon field on parallelepipeds of large volume \(a_N (\lim \frac{{a_N }}{{\log N}} = \infty ,\lim \frac{{\log \frac{N}{{a_N }}}}{{\log _2 N}} = \infty )\). We consider random fields with finite moment-generating function in a right neighborhood of zero. Bibliography: 8 titles.