Multiple Zeta Functions and High-Dimensional Random Walks

Takahiro Aoyama

It is quite challenging to ascertain whether a certain multivariable function is a characteristic function when its corresponding measure is not trivial to be or not to be a probability measure on R^d. In this article, we formulate multi-zeta function-based high-dimensional discrete probability distributions with infinitely many mass points on Z^d and Z^d-valued random walks given by those convolutions in terms of multiple zeta functions. In particular, a necessary and sufficient condition is provided for some polynomial finite Euler products to yield characteristic functions.

Bulletin of the Japan Society Industrial and Applied Mathematics

Japan Society Industrial and Applied Mathematics

33

2

62

71

https://doi.org/10.11540/bjsiam.33.2_62