Cox process

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.

is called a Cox process directed by

( η ∣ ξ = μ )

is a Poisson process with intensity measure

is a Cox process directed by

has the Laplace transform for any positive, measurable function

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