Equilibrium unfolding - Revision history

en>Monkbot: /* Other forms of denaturation */Task 2: Fix CS1 deprecated coauthor parameter errors

2014-07-17T01:08:09Z

Other forms of denaturation: Task 2: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 03:08, 17 July 2014
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	In [~~[mathematics~~]~~], a '''sample-continuous process'''~~ is a [~~[stochastic process]] whose sample paths are [[almost surely]] [[continuous function]]s~~.		Hello buddy. Allow me introduce myself. I am [http://Www.dmv.org/buy-sell/auto-warranty/extended-warranty.php Luther Aubrey]. Managing individuals is extended [http://nationalheritagemuseum.org/UserProfile/tabid/43/userId/31686/Default.aspx car warranty] what I do in my working day job. Her family members lives in Delaware but extended car warranty she needs to transfer simply because of her family members. One of the [http://Www.Motortrend.com/new_cars/auto_warranty/ issues I] adore most is [http://Www.Consumer.ftc.gov/articles/0054-auto-service-contracts-and-warranties greeting card] collecting but auto warranty I don't have the time lately.<br><br>Also visit my weblog; [http://www.skyperoom.com/blogs/post/9816 extended auto warranty] car warranty ([http://www.Nurcac.org/UserProfile/tabid/43/userId/18128/Default.aspx link web page])

	~~==Definition==~~

	~~Let (Ω, Σ, '''P''') be a [[probability space]]~~. ~~Let ''X'' : ''I'' × Ω → ''S'' be a stochastic process, where the [[index set~~]~~] ''~~I~~'' and state space ''S'' are both [[topological space]]s~~. ~~Then the process ''X'' is called '''sample-continuous''' (or '''almost surely continuous''', or~~ simply ~~'''continuous''') if~~ the ~~map ''X''(''ω'') ~~:~~ ''I'' → ''S'' is [[Continuous function (topology)\|continuous as a function of topological spaces]] for '''P'''-[[almost all]] ''ω'' in ''Ω''~~.

	~~In many examples, the index set ''~~I~~'' is an interval of time, [0, ''T''~~] ~~or [0, +∞), and the state space ''S''~~ is ~~the~~ [~~[real line]] or ''n''-[[dimension]]al [[Euclidean space]] '''R'''<sup>''n''<~~/~~sup>~~.

	~~==Examples==~~

	* [[Brownian motion]] (the [[Wiener process]]) on Euclidean space is sample-~~continuous.~~
	* For "nice" parameters of the equations, solutions to [[stochastic differential equation]]s are sample-~~continuous. See the existence~~ and ~~uniqueness theorem in~~ the ~~stochastic differential equations article for some sufficient conditions to ensure sample continuity~~.
	* The process ''X'' : [0, +∞) × Ω → '''R''' that makes equiprobable jumps up or down every unit time according to

	::<~~math~~>~~\begin{cases} X_{t} \sim \mathrm{Unif} (\{X_{t-1} - 1, X_{t-1} + 1\}), & t \mbox{ an integer;} \\ X_{t} = X_{\lfloor t \rfloor}, & t \mbox{ not an integer;} \end{cases}~~<~~/math~~>

	: ~~is ''not'' sample-continuous~~. ~~In fact, it is surely discontinuous~~.

	~~==Properties==~~

	* For sample-continuous processes, the [[finite-dimensional distribution]~~]s determine the~~ [~~[Law (stochastic processes)\|law]], and vice versa~~.

	~~==See also==~~

	* [[Continuous stochastic process]]

	~~==References==~~

	* {{cite book
	~~\| author = Kloeden, Peter E.~~
	~~\|coauthors = Platen, Eckhard~~
	~~\| title = Numerical solution of stochastic differential equations~~
	~~\| series = Applications of Mathematics (New York~~) 23
	~~\|publisher = Springer-Verlag~~
	~~\| location = Berlin~~
	~~\| year = 1992~~
	~~\| pages = 38–39;~~
	~~\| isbn = 3-540-54062-8~~
	}}

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

128.61.115.251: /* Chemical denaturation */

2013-11-19T07:56:52Z

Chemical denaturation

← Older revision		Revision as of 09:56, 19 November 2013
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	~~Friends contact him Royal~~. ~~Delaware~~ is the ~~only location~~ I'~~ve been residing~~ in. ~~One~~ of ~~his favorite hobbies~~ is ~~playing crochet but he hasn~~'~~t made a dime with it~~. ~~Interviewing~~ is ~~how I make a living~~ and ~~it's~~ some ~~thing I really appreciate~~.<br><br>~~my webpage~~ ... [~~http://christianculturecenter~~.~~org/ActivityFeed/MyProfile/tabid/61/userId/34117/Default.aspx http~~:~~//christianculturecenter.org/~~]		In [[mathematics]], a '''sample-continuous process''' is a [[stochastic process]] whose sample paths are [[almost surely]] [[continuous function]]s.

			==Definition==

			Let (Ω, Σ, '''P''') be a [[probability space]]. Let ''X'' : ''I'' × Ω → ''S'' be a stochastic process, where the [[index set]] ''I'' and state space ''S'' are both [[topological space]]s. Then the process ''X'' is called '''sample-continuous''' (or '''almost surely continuous''', or simply '''continuous''') if the map ''X''(''ω'') : ''I'' → ''S'' is [[Continuous function (topology)\|continuous as a function of topological spaces]] for '''P'''-[[almost all]] ''ω'' in ''Ω''.

			In many examples, the index set ''I'' is an interval of time, [0, ''T''] or [0, +∞), and the state space ''S'' is the [[real line]] or ''n''-[[dimension]]al [[Euclidean space]] '''R'''<sup>''n''</sup>.

			==Examples==

			* [[Brownian motion]] (the [[Wiener process]]) on Euclidean space is sample-continuous.
			* For "nice" parameters of the equations, solutions to [[stochastic differential equation]]s are sample-continuous. See the existence and uniqueness theorem in the stochastic differential equations article for some sufficient conditions to ensure sample continuity.
			* The process ''X'' : [0, +∞) × Ω → '''R''' that makes equiprobable jumps up or down every unit time according to

			::<math>\begin{cases} X_{t} \sim \mathrm{Unif} (\{X_{t-1} - 1, X_{t-1} + 1\}), & t \mbox{ an integer;} \\ X_{t} = X_{\lfloor t \rfloor}, & t \mbox{ not an integer;} \end{cases}</math>

			: is ''not'' sample-continuous. In fact, it is surely discontinuous.

			==Properties==

			* For sample-continuous processes, the [[finite-dimensional distribution]]s determine the [[Law (stochastic processes)\|law]], and vice versa.

			==See also==

			* [[Continuous stochastic process]]

			==References==

			* {{cite book
			\| author = Kloeden, Peter E.
			\|coauthors = Platen, Eckhard
			\| title = Numerical solution of stochastic differential equations
			\| series = Applications of Mathematics (New York) 23
			\|publisher = Springer-Verlag
			\| location = Berlin
			\| year = 1992
			\| pages = 38–39;
			\| isbn = 3-540-54062-8
			}}

			[[Category:Stochastic processes]]

en>FrescoBot: Bot: link syntax/spacing

2012-02-21T06:13:36Z

Bot: link syntax/spacing

New page

Friends contact him Royal. Delaware is the only location I've been residing in. One of his favorite hobbies is playing crochet but he hasn't made a dime with it. Interviewing is how I make a living and it's some thing I really appreciate.<br><br>my webpage ... [http://christianculturecenter.org/ActivityFeed/MyProfile/tabid/61/userId/34117/Default.aspx http://christianculturecenter.org/]