Cox process
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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.^{[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]}
See also
- Poisson hidden Markov model
- Doubly stochastic model
- Inhomogeneous Poisson process, where λ(t) is restricted to a deterministic function
- Ross's conjecture
- Gaussian process
References
- Notes
- ↑ Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
- ↑ Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
- ↑ Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
- Bibliography
- 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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