I’ve been trying to find information on the following situation but I have not been able to find much (if anything) about it. I was wondering if someone could maybe direct me to papers/books that discuss the following.
Say on a lattice $\mathbb{Z}^d$ we have a random variable $X$ that has a Poisson($\lambda$) distribution that indicates how many of a particle exist at a certain $x \in \mathbb{Z}^d$.
Now what happens if $\lambda$ is dependent on $x$? Of course this is simple to interpret but I am looking for some kind of source that works with this assumption and maybe shows some properties or even just discusses it at all.
If anyone could help me I would be very grateful, thanks!