In probability theory, a **Cox process**, also known as a **doubly stochastic Poisson process** is a point process which is a generalization of a Poisson process where the intensity that varies across the underlying mathematical space (often space or time) is itself a stochastic process. The process is named after the statistician David Cox, who first published the model in 1955.^{[1]}

Cox processes are used to generate simulations of spike trains (the sequence of action potentials generated by a neuron),^{[2]} and also in financial mathematics where they produce a "useful framework for modeling prices of financial instruments in which credit risk is a significant factor."^{[3]}

Let be a random measure.

A random measure is called a Cox process directed by , if is a Poisson process with intensity measure .

Here, is the conditional distribution of , given .

If is a Cox process directed by , then has the Laplace transform

for any positive, measurable function .