Permanental Processes

TL;DR

This paper surveys permanental processes, a class of stochastic processes generalizing squared Gaussian processes, highlighting their theoretical foundations and open research problems.

Contribution

It introduces permanental processes as a new research area, extending Gaussian process theory to non-symmetric, non-positive definite functions.

Findings

Permanental processes generalize squared Gaussian processes.

Many open problems remain in the theory of permanental processes.

Abstract

This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian process is replaced by a function that is not necessarily symmetric nor positive definite, but that nevertheless determines a stochastic process. This is a new avenue of research with very many open problems.