“Cox process”的意思、由来-开放百科全书

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Cox process

释义

Definition
Laplace transform
See also
References

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 time-dependent intensity 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]

Definition

Let be a random measure.

A random measure is called a Cox process directed by , if is a Poisson process with intensity measure .

Here, is the conditional distribution of , given .

Laplace transform

If is a Cox process directed by , then has the Laplace transform

for any positive, measurable function .

References

Notes

1. ^{{Cite journal | last1 = Cox | first1 = D. R. | authorlink = David Cox (statistician)| title = Some Statistical Methods Connected with Series of Events | journal = Journal of the Royal Statistical Society | volume = 17 | issue = 2 | pages = 129–164 | doi = 10.2307/2983950| year = 1955 | pmid = | pmc = }}
2. ^{{Cite journal | last1 = Krumin | first1 = M. | last2 = Shoham | first2 = S. | doi = 10.1162/neco.2009.08-08-847 | title = Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions | journal = Neural Computation | volume = 21 | issue = 6 | pages = 1642–1664 | year = 2009 | pmid = 19191596| pmc = }}
3. ^{{Cite journal | last1 = Lando | first1 = David| title = On cox processes and credit risky securities | doi = 10.1007/BF01531332 | journal = Review of Derivatives Research | volume = 2 | issue = 2–3 | pages = 99–120| year = 1998 | pmid = | pmc = }}

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)

1 : Poisson point processes

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Definition

Laplace transform

See also

References