From what I understand (and I am not an expert in probability), a "point process" on a set $X$ is a probability measure on $2^X$, the set of subsets of $X$. I only want to consider the case when $X$ is finite. In particular, I have been interested recently in determinantal processes, where probabilities are given by the minors of a matrix (the "kernel" of the process).
I am wondering if there is a name for the similar notion for multisets? That is, we fix some positive integer $m$, and consider a probability measure on the set of multisets whose elements come from $X$, and where each $x \in X$ is allowed to occur with multiplicity at most $m$.
Also is there something similar to the notion of determinantal processes in this case with multisets?