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77.13.153.58: /* Rotors */

2014-11-11T09:22:11Z

Rotors

← Older revision		Revision as of 11:22, 11 November 2014
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	~~In [[probability theory]], a '''random measure''~~' is ~~a [[measure (mathematics)\|measure]]-valued [[random element]]~~.~~<ref name="RN">[[Olav Kallenberg\|Kallenberg, O.]],~~ '~~'Random Measures'', 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin (1986). ISBN 0-12-394960-2 {{MR\|854102}}. An authoritative~~ but ~~rather difficult reference.~~		The writer's title is Christy. For many years she's been living in Kentucky but her spouse desires them to transfer. Distributing production is where her primary earnings arrives from. One of the very best things in the globe for him is doing ballet and he'll be beginning some thing else alongside with it.<br><br>Feel free to visit my weblog: [http://formalarmour.com/index.php?do=/profile-26947/info/ spirit messages]

	</ref><ref name="G">Jan Grandell, Point processes and random measures, ''Advances in Applied Probability'' 9 (1977) 502-526. {{MR\|0478331}} [http://links.jstor.org/sici?sici=0001-8678%28197709%299%3A3%3C502%3APPARM%3E2.0.~~CO%3B2-5 JSTOR] A nice and clear introduction.~~

	~~</ref> Let X be a complete separable metric space and <math>\mathfrak{B}(X)</math> the [[Sigma-algebra#Generated .CF.83-algebra\|σ-algebra]] of its Borel sets. A [[Borel measure]] μ on X~~ is ~~boundedly finite if μ(A) < ∞ for every bounded Borel set A~~. ~~Let <math>M_X</math> be the space~~ of ~~all boundedly finite measures on <math>\mathfrak{B}(X)</math>. Let {{nowrap\|(Ω, ℱ, ''P'')}} be a [[probability space]], then a random measure maps from this probability space to~~ the ~~[[measurable space]] {{nowrap\|(<math>M_X</math>, <math>\mathfrak{B}(M_X)</math>)}}.<ref name="daleyPPI2003">{{cite doi\|10.1007/b97277}}</ref>A measure generally might be decomposed as:~~

	~~:<math> \mu=\mu_d + \mu_a = \mu_d + \sum_{n=1}^N \kappa_n \delta_{X_n}, </math>~~

	~~Here <math>\mu_d</math> is a diffuse measure without atoms, while <math>\mu_a</math> is a purely atomic measure.~~

	~~==Random counting measure==~~
	~~A random measure of~~ the ~~form:~~

	~~:<math> \mu=\sum_{n=1}^N \delta_{X_n}, </math>~~

	~~where <math>\delta</math>~~ is ~~the [[Dirac measure]],~~ and ~~<math>X_n</math> are random variables, is called a ''[[point process]]'~~'<~~ref name="RN"/~~><~~ref name="G"/~~> or [~~[random counting measure]]. This random measure describes the set of ''N'' particles, whose locations are given by the (generally vector valued) random variables <math>X_n<~~/~~math>. The diffuse component <math>\mu_d<~~/~~math> is null for a counting measure~~.

	~~In the formal notation of above a random counting measure is a map from a probability space to the measurable space {{nowrap\|(<math>N_X<~~/~~math>, <math>\mathfrak{B}(N_X)</math>)}} a [[measurable space]]~~. ~~Here <math>N_X<~~/~~math> is the space of all boundedly finite integer~~-~~valued measures <math>N \in M_X<~~/~~math> (called counting measures).~~

	The definitions of expectation measure, Laplace functional, moment measures and stationarity for random measures follow those of [[point process]]es. Random measures are useful in the description and analysis of [[Monte Carlo method]]s, such as [[numerical quadrature#Monte Carlo\|Monte Carlo numerical quadrature]] and [[particle filter]]s.<ref>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</ref>

	~~==See also==~~
	* [[Point process]]
	* [[Poisson random measure]]
	* [[Random element]]
	* [[Vector measure]]
	* [[Distribution ensemble\|Ensemble]]

	~~==References==~~
	~~<references~~/>

	~~[[Category:Measures (measure theory)~~]]
	~~[[Category:Stochastic processes]]~~


	~~{{probability-stub}}~~

en>Rjwilmsi: Citation parameter fixes, using AWB (9382)

2013-08-05T12:46:34Z

Citation parameter fixes, using AWB (9382)

← Older revision		Revision as of 14:46, 5 August 2013
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	~~Hello buddy~~. ~~Let me introduce myself~~. ~~I am Luther Aubrey~~. ~~Years~~ in the ~~past we moved to Arizona but my wife wants us to move~~. ~~Interviewing~~ is ~~what she does but soon she'll~~ be on ~~her own~~. ~~The favorite pastime for my kids and me is dancing and now I~~'~~m attempting~~ to ~~make money with it~~.<br><br>~~Also visit my website~~ :: [~~http:~~//~~112~~.~~217~~.~~168~~.~~194~~/~~onsesang~~/xe/~~index~~.~~php?document_srl~~=~~10158&mid~~=~~comm_info01 auto warranty~~]		In [[probability theory]], a '''random measure''' is a [[measure (mathematics)\|measure]]-valued [[random element]].<ref name="RN">[[Olav Kallenberg\|Kallenberg, O.]], ''Random Measures'', 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin (1986). ISBN 0-12-394960-2 {{MR\|854102}}. An authoritative but rather difficult reference.

			</ref><ref name="G">Jan Grandell, Point processes and random measures, ''Advances in Applied Probability'' 9 (1977) 502-526. {{MR\|0478331}} [http://links.jstor.org/sici?sici=0001-8678%28197709%299%3A3%3C502%3APPARM%3E2.0.CO%3B2-5 JSTOR] A nice and clear introduction.

			</ref> Let X be a complete separable metric space and <math>\mathfrak{B}(X)</math> the [[Sigma-algebra#Generated .CF.83-algebra\|σ-algebra]] of its Borel sets. A [[Borel measure]] μ on X is boundedly finite if μ(A) < ∞ for every bounded Borel set A. Let <math>M_X</math> be the space of all boundedly finite measures on <math>\mathfrak{B}(X)</math>. Let {{nowrap\|(Ω, ℱ, ''P'')}} be a [[probability space]], then a random measure maps from this probability space to the [[measurable space]] {{nowrap\|(<math>M_X</math>, <math>\mathfrak{B}(M_X)</math>)}}.<ref name="daleyPPI2003">{{cite doi\|10.1007/b97277}}</ref>A measure generally might be decomposed as:

			:<math> \mu=\mu_d + \mu_a = \mu_d + \sum_{n=1}^N \kappa_n \delta_{X_n}, </math>

			Here <math>\mu_d</math> is a diffuse measure without atoms, while <math>\mu_a</math> is a purely atomic measure.

			==Random counting measure==
			A random measure of the form:

			:<math> \mu=\sum_{n=1}^N \delta_{X_n}, </math>

			where <math>\delta</math> is the [[Dirac measure]], and <math>X_n</math> are random variables, is called a ''[[point process]]''<ref name="RN"/><ref name="G"/> or [[random counting measure]]. This random measure describes the set of ''N'' particles, whose locations are given by the (generally vector valued) random variables <math>X_n</math>. The diffuse component <math>\mu_d</math> is null for a counting measure.

			In the formal notation of above a random counting measure is a map from a probability space to the measurable space {{nowrap\|(<math>N_X</math>, <math>\mathfrak{B}(N_X)</math>)}} a [[measurable space]]. Here <math>N_X</math> is the space of all boundedly finite integer-valued measures <math>N \in M_X</math> (called counting measures).

			The definitions of expectation measure, Laplace functional, moment measures and stationarity for random measures follow those of [[point process]]es. Random measures are useful in the description and analysis of [[Monte Carlo method]]s, such as [[numerical quadrature#Monte Carlo\|Monte Carlo numerical quadrature]] and [[particle filter]]s.<ref>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</ref>

			==See also==
			* [[Point process]]
			* [[Poisson random measure]]
			* [[Random element]]
			* [[Vector measure]]
			* [[Distribution ensemble\|Ensemble]]

			==References==
			<references/>

			[[Category:Measures (measure theory)]]
			[[Category:Stochastic processes]]


			{{probability-stub}}

en>Phil Boswell: convert dodgy URL to ID, replaced: url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.612&rep=rep1&type=pdf → id = {{citeseerx|10.1.1.45.612}} using AWB

2012-07-14T11:39:21Z

convert dodgy URL to ID, replaced: url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.45.612&rep=rep1&type=pdf → id = {{citeseerx|10.1.1.45.612}} using AWB

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Hello buddy. Let me introduce myself. I am Luther Aubrey. Years in the past we moved to Arizona but my wife wants us to move. Interviewing is what she does but soon she'll be on her own. The favorite pastime for my kids and me is dancing and now I'm attempting to make money with it.<br><br>Also visit my website :: [http://112.217.168.194/onsesang/xe/index.php?document_srl=10158&mid=comm_info01 auto warranty]