Cox process

A Cox process (named after the statistician Sir David Cox), also known as a doubly stochastic Poisson process or mixed Poisson process, is a stochastic process which is a generalization of a Poisson process. In the case of Cox processes, the time-dependent intensity λ(t) is a stochastic process which is separated from the Poisson process.

An example would be a spike train of a sensory neuron with external stimulation. If the stimulation is a stochastic process and it modulates the firing rate (intensity function) of the neuron, then the spike train can be thought of as a realization of a Cox process.

Another example of the use of Cox processes is in financial mathematics for modeling Credit risk.

See also

• Poisson hidden Markov model
• Doubly stochastic model

References

• Cox, D. R. Some statistical methods connected with series of events. J. R. Statist. Soc. Ser. B 17, 129-164, 1955.
• Cox, D. R. and Isham, V. Point Processes, London: Chapman & Hall, 1980 ISBN 0-412-21910-7
• Donald L. Snyder and Michael I. Miller Random Point Processes in Time and Space Springer-Verlag, 1991 ISBN 0-387-97577-2 (New York) ISBN 3-540-97577-2 (Berlin)

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