Permanental Processes with Kernels That Are Not Equivalent to a Symmetric Matrix

Abstract

Kernels of α-permanental processes of the form

$$\displaystyle \begin{aligned} \widetilde u(x,y)=u(x,y)+f(y),\qquad x,y\in S, \end{aligned} $$

(15.1)

which u(x, y) is symmetric, and f is an excessive function for the Borel right process with potential densities u(x, y), are considered. Conditions are given that determine whether $\{\widetilde u(x,y);x,y\in S\}$ is symmetrizable or asymptotically symmetrizable.