On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality

Abstract

Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to higher dimensional random variables. To obtain this result, a higher dimensional analogue of the Berry-Esseen inequality is proved, generalising a two-dimensional version of Sadikova.

arXiv commentExtended Abstract for the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms. For full proofs see arXiv:1602.04055v1 [math.PR]