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]

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Notes
  1. ^ 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.  edit
  2. ^ 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.  edit
  3. ^ Lando, David (1998). "On cox processes and credit risky securities". Review of Derivatives Research 2 (2–3): 99–12. doi:10.1007/BF01531332.  edit
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