Strong limit theorems for quasi-orthogonal random fields

F. Móricz

Journal of Multivariate Analysis, 1989, vol. 30, issue 2, 255-278

Abstract: This is a systematic and unified treatment of a variety of seemingly different strong limit problems. The main emphasis is laid on the study of the a.s. behavior of the rectangular means [zeta]mn = 1/([lambda]1(m) [lambda]2(n)) [Sigma]i=1m [Sigma]k=1n Xik as either max{m, n} --> [infinity] or min{m, n} --> [infinity]. Here {Xik: i, k >= 1} is an orthogonal or merely quasi-orthogonal random field, whereas {[lambda]1(m): m >= 1} and {[lambda]2(n): n >= 1} are nondecreasing sequences of positive numbers subject to certain growth conditions. The method applied provides the rate of convergence, as well. The sufficient conditions obtained are shown to be the best possible in general. Results on double subsequences and 1-parameter limit theorems are also included.

Keywords: orthogonal; and; quasi-orthogonal; random; fields; two-parameter; limit; theorems; SLLN; for; rectangular; means; rate; of; convergence; double; subsequences; one-parameter; limit; theorems; SLLN; for; square; means; and; spherical; means (search for similar items in EconPapers)
Date: 1989
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