- Random measure
In

probability theory , a**random measure**is a measure-valuedrandom element .Kallenberg, O., "Random Measures", 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin (1986). ISBN 0-123-94960-2 [*http://www.ams.org/mathscinet-getitem?mr=854102 MR854102*] . An authoritative but rather difficult reference.] A random measure of the form

:$mu=sum\_\{n=1\}^N\; delta\_\{X\_n\},$

where $delta$ is the

Dirac measure , and $X\_n$ are random variables, is called a "point process " orrandom counting measure . This random measure describes the set of "N" particles, whose locations are given by the (generally vector valued) random variables $X\_n$. Random measures are useful in the description and analysis ofMonte Carlo method s, such as Monte Carlo numerical quadrature andparticle filter s [*Crisan, D., "Particle Filters: A Theoretical Perspective", in "Sequential Monte Carlo in Practice," Doucet, A., de Freitas, N. and Gordon, N. (Eds), Springer, 2001, ISBN 0-387-95146-6*] .**ee also***

Point process

*Poisson random measure

*Random element

*Vector measure

* Ensemble**References**

*Wikimedia Foundation.
2010.*

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