In probability theory, a Cox process, also known as a doubly stochastic Poisson process or mixed Poisson process, is a stochastic process which is a generalization of a Poisson process where the time-dependent intensity λ(t) is itself a stochastic process. The process is named after the statistician David Cox, who first published the model in 1955.
Cox processes are used to generate simulations of spike trains (the sequence of action potentials generated by a neuron), 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."
- Poisson hidden Markov model
- Doubly stochastic model
- Inhomogeneous Poisson process, where λ(t) is restricted to a deterministic function
- Ross's conjecture
- Gaussian process
- Cox, D. R. (1955). "Some Statistical Methods Connected with Series of Events". Journal of the Royal Statistical Society 17 (2): 129–164. doi:10.2307/2983950.
- Krumin, M.; Shoham, S. (2009). "Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions". Neural Computation 21 (6): 1642–1664. doi:10.1162/neco.2009.08-08-847. PMID 19191596.
- Lando, David (1998). "On cox processes and credit risky securities". Review of Derivatives Research 2 (2–3): 99–12. doi:10.1007/BF01531332.
- 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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