Market›Cox process
Company Profile

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 is itself a stochastic process. The process is named after the statistician David Cox, who first published the model in 1955.

Definition
Let \xi be a random measure. A random measure \eta is called a Cox process directed by \xi , if \mathcal L(\eta \mid \xi=\mu) is a Poisson process with intensity measure \mu . Here, \mathcal L(\eta \mid \xi=\mu) is the conditional distribution of \eta , given \{ \xi=\mu\} . == Laplace transform ==
Laplace transform
If \eta is a Cox process directed by \xi , then \eta has the Laplace transform : \mathcal L_\eta(f)=\exp \left(- \int 1-\exp(-f(x))\; \xi(\mathrm dx)\right) for any positive, measurable function f . ==See also==
Source: Wikipedia ↗
tickerdossier.comtickerdossier.substack.com