Laws of iterated logarithm of multiparameter wiener processes

Let {} denote the N-parameter Wiener process on . 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 , c >= 0, is obtained where DN = [Pi]k = 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.Multiparameter Wiener process Brownian motion separable stochastic process joint normal distribution law of iterated logarithm