Additive identity - Revision history

en>Cydebot: Robot - Moving category Zero to :Category:0 (number) per CFD at Wikipedia:Categories for discussion/Log/2014 November 19.

2014-11-28T21:59:06Z

Robot - Moving category Zero to Category:0 (number) per CFD at Wikipedia:Categories for discussion/Log/2014 November 19.

← Older revision		Revision as of 23:59, 28 November 2014
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	~~{{About\|bivariate processes\|arrival processes to queues\|Markovian arrival process}}~~		Hi there. Allow me start by introducing the writer, her title is Sophia Boon but she by no means truly favored that title. He functions as a bookkeeper. For many years he's been residing in Alaska and he doesn't plan on changing it. She is truly fond of caving but she doesn't have the time lately.<br><br>My web blog - free psychic readings ([http://brazil.amor-amore.com/irboothe Suggested Browsing])
	~~In [[applied probability]]~~, ~~a '''Markov additive process''' ('''MAP''')~~ is ~~a bivariate [[Markov process]] where the future states depends only on one of the variables~~.~~<ref name="magiera" />~~

	~~==Definition==~~

	~~===Finite or countable state space for ''J''(''t'')===~~

	~~The process {(''X''(''t''),''J''(''t'')) : ''t'' ≥ 0} is~~ a ~~Markov additive process with continuous time parameter ''t'' if<ref name="magiera">{{cite doi\|10~~.~~1007/978-1-4612-2234-7_12}}</ref>~~

	~~# {(''X''(''t''),''J''(''t'')) : ''t'' ≥ 0} is a [[Markov process]]~~
	~~# the conditional distribution of (''X''(''t'' + '~~'s~~'') − ''X''(''t''),''J''(''s'' + '~~'t~~'')) given (''X''(''s''),''J''(''s'')) depends only~~ on ~~''J''(''s'')~~.

	~~The state space of the process~~ is ~~'''R''' × ''S'' where ''X''(''t'') takes real values and ''J''(''t'') takes values in some countable set ''S''.~~

	~~===General state space for ''J''(''t'')===~~

	~~For the case where ''J''(''t'') takes a more general state space the evolution~~ of ~~''X''('~~'t~~'') is governed by ''J''(''t'') in~~ the ~~sense that for any ''f'' and ''g'' we require<ref>{{cite doi\|10~~.~~1007/0-387-21525-5_11}}~~<~~/ref~~>

	::<~~math~~>~~\mathbb E[f(X_{t+s}~~-~~X_t)g~~(~~J_{t+s})\|\mathcal F_t] = \mathbb E_{J_t,0}~~[~~f(X_s)g(J_s)]<~~/~~math>~~.

	~~==Example==~~

	~~A [[fluid queue]] is a Markov additive process where ''J''(''t'') is a [[continuous~~-~~time Markov chain]]~~.

	~~==Applications==~~

	Çinlar uses the unique structure of the MAP to prove that, given a [[gamma process]] with a shape parameter that is a function of [[Brownian motion]], the resulting lifetime is distributed according to the [[Weibull distribution]].

	Kharoufeh presents a compact transform expression for the failure distribution for wear processes of a component degrading according to a Markovian environment inducing state-dependent continuous linear wear by using the properties of a MAP and assuming the wear process to be temporally homogeneous and that the environmental process has a finite [[state space]].

	~~==Notes==~~
	~~{{Reflist}}~~

	~~{{Stochastic processes}}~~
	~~{{probability-stub}}~~

	~~[[Category:Stochastic processes]~~]

178.16.9.65: /* The additive identity annihilates ring elements */

2013-11-24T22:55:24Z

The additive identity annihilates ring elements

← Older revision		Revision as of 00:55, 25 November 2013
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	The ~~author~~'s name is ~~Christy Brookins~~. ~~Office supervising~~ is ~~my occupation. I~~'~~ve always loved residing~~ in ~~Alaska~~. ~~Doing ballet~~ is ~~some thing she would never give up~~.<br><br>~~my weblog~~ - [~~http:~~/~~/checkmates~~.co.~~za/index~~.~~php?do~~=~~/profile~~-~~56347/info/ best psychics~~]		{{About\|bivariate processes\|arrival processes to queues\|Markovian arrival process}}
			In [[applied probability]], a '''Markov additive process''' ('''MAP''') is a bivariate [[Markov process]] where the future states depends only on one of the variables.<ref name="magiera" />

			==Definition==

			===Finite or countable state space for ''J''(''t'')===

			The process {(''X''(''t''),''J''(''t'')) : ''t'' ≥ 0} is a Markov additive process with continuous time parameter ''t'' if<ref name="magiera">{{cite doi\|10.1007/978-1-4612-2234-7_12}}</ref>

			# {(''X''(''t''),''J''(''t'')) : ''t'' ≥ 0} is a [[Markov process]]
			# the conditional distribution of (''X''(''t'' + ''s'') − ''X''(''t''),''J''(''s'' + ''t'')) given (''X''(''s''),''J''(''s'')) depends only on ''J''(''s'').

			The state space of the process is '''R''' × ''S'' where ''X''(''t'') takes real values and ''J''(''t'') takes values in some countable set ''S''.

			===General state space for ''J''(''t'')===

			For the case where ''J''(''t'') takes a more general state space the evolution of ''X''(''t'') is governed by ''J''(''t'') in the sense that for any ''f'' and ''g'' we require<ref>{{cite doi\|10.1007/0-387-21525-5_11}}</ref>

			::<math>\mathbb E[f(X_{t+s}-X_t)g(J_{t+s})\|\mathcal F_t] = \mathbb E_{J_t,0}[f(X_s)g(J_s)]</math>.

			==Example==

			A [[fluid queue]] is a Markov additive process where ''J''(''t'') is a [[continuous-time Markov chain]].

			==Applications==

			Çinlar uses the unique structure of the MAP to prove that, given a [[gamma process]] with a shape parameter that is a function of [[Brownian motion]], the resulting lifetime is distributed according to the [[Weibull distribution]].

			Kharoufeh presents a compact transform expression for the failure distribution for wear processes of a component degrading according to a Markovian environment inducing state-dependent continuous linear wear by using the properties of a MAP and assuming the wear process to be temporally homogeneous and that the environmental process has a finite [[state space]].

			==Notes==
			{{Reflist}}

			{{Stochastic processes}}
			{{probability-stub}}

			[[Category:Stochastic processes]]

en>GrouchoBot: r2.7.2) (Robot: Adding ta:கூட்டல் முற்றொருமை

2012-06-05T09:33:36Z

r2.7.2) (Robot: Adding ta:கூட்டல் முற்றொருமை

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The author's name is Christy Brookins. Office supervising is my occupation. I've always loved residing in Alaska. Doing ballet is some thing she would never give up.<br><br>my weblog - [http://checkmates.co.za/index.php?do=/profile-56347/info/ best psychics]