In probability theory, a Laplace functional refers to one of two possible mathematical functions of functions or, more precisely, functionals that serve as mathematical tools for studying either point processes or concentration of measure properties of metric spaces. One type of Laplace functional,[1][2] also known as a characteristic functional[a] is defined in relation to a point process, which can be interpreted as random counting measures, and has applications in characterizing and deriving results on point processes.[5] Its definition is analogous to a characteristic function for a random variable.
The other Laplace functional is for probability spaces equipped with metrics and is used to study the concentration of measure properties of the space.
- ^ a b D. Stoyan, W. S. Kendall, and J. Mecke. Stochastic geometry and its applications, volume 2. Wiley, 1995.
- ^ a b D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, Springer, New York, second edition, 2003.
- ^ Kingman, John (1993). Poisson Processes. Oxford Science Publications. p. 28. ISBN 0-19-853693-3.
- ^ Baccelli, F. O. (2009). "Stochastic Geometry and Wireless Networks: Volume I Theory" (PDF). Foundations and Trends in Networking. 3 (3–4): 249–449. doi:10.1561/1300000006.
- ^ Barrett J. F. The use of characteristic functionals and cumulant generating functionals to discuss the effect of noise in linear systems, J. Sound & Vibration 1964 vol.1, no.3, pp. 229-238
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