Laws of iterated logarithm of multiparameter wiener processes

AbstractLet {X(t) : t ∈ R+N} denote the N-parameter Wiener process on R+N = [0, ∞)n. For multiple sequences of certain independent random variables the authors find lower bounds for the distributions of maximum of partial sums of these random variables, and as a consequence a useful upper bound for the yet unknown function P{supt∈DnX(t) ≥ c}, c ≥ 0, is obtained where DN = Πk = 1N [0, Tk]. The latter bound is used to give three different varieties of N-parameter generalization of the classical law of iterated logarithm for the standard Brownian motion process