Wat is Inhomogeneous Poisson process, Cox process?

An inhomogeneous Poisson process has a deterministic intensity $\lambda(t)$: counts in disjoint intervals are independent Poisson with means $\int\lambda(t)\,dt$. A Cox process (doubly stochastic Poisson process) is a Poisson process whose intensity is itself a random process, independent of the events it drives.