Abstract
In the studies of mathematical statistics, we often consider discrete distributions and their corresponding stochastic processes. Especially, probabilistic limit theorems of them may give us some progress in mathematical finance. There exist not so many properties of discrete distributions on $\mathbb{R}^d$. In this paper, we treat multiple zeta functions as to define several forms of discrete distributions on $\mathbb{R}^d$ including those with infinitely many mass points. Our purpose is to obtain new methods in the relations between multiple infinite series and high dimensional integral calculus, which can provide us more opportunities to handle high dimensional phenomenon.
