Median graph - Revision history

en>DisillusionedBitterAndKnackered: LoC, Copac and many other book sources have it spelt correctly. Amazon has it listed wrong, but right on their cover illustration. Why keep it wrong here?

2014-11-27T22:30:02Z

LoC, Copac and many other book sources have it spelt correctly. Amazon has it listed wrong, but right on their cover illustration. Why keep it wrong here?

← Older revision		Revision as of 00:30, 28 November 2014
Line 1:		Line 1:
	By investing in a premium Word - Press theme, you're investing in the future of your website. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. Should you go with simple HTML or use a platform like Wordpress. Keep reading for some great Word - Press ideas you can start using today. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site. <br><br>

	~~These folders as well as files have to copied and~~ the ~~saved. After all, Word - Press is free, many~~ of the ~~enhancements~~ for ~~Word - Press like themes and plugins~~ are ~~also free~~, and ~~there is plenty of free information online about how to use Word - Press~~. ~~We also help to integrate various plug-ins to expand~~ the ~~functionalities of~~ the ~~web application~~. ~~This is identical to doing~~ a ~~research as in depth above~~, ~~nevertheless~~ you can ~~see various statistical details like the number of downloads~~ and ~~when the template was not long ago updated. Many times the camera is following Mia, taking in her point of view in almost every frame~~. <br><br>~~You can down load it here at this link: and utilize your FTP software program~~ to ~~upload it to your~~ Word - Press ~~Plugin folder~~. ~~The~~ only ~~problem with most is that they only offer a monthly plan, you never own~~ the ~~software and you can’t even install~~ the ~~software on~~ your ~~site, you must go~~ to ~~another website~~ to ~~manage your list~~ and ~~edit your autoresponder~~. ~~If you adored~~ this ~~article therefore you would like~~ to ~~acquire more info relating~~ to ~~[http://GET7~~.~~pw/wordpress_backup_plugin_891441 wordpress backup] please visit our web-site. Setting Up Your Business Online Using Free Wordpress Websites. Enough automated blog posts plus a system keeps~~ you and ~~your clients happy. For any web design~~ and ~~development assignment, this is definitely one of~~ the ~~key concerns, specifically for online retail outlets as well as e-commerce websites~~. <br><br>~~The primary differences~~ are in the plugins ~~that I install, as all sites don't need all the normal plugins. High Quality Services: These companies help you~~ in ~~creating high quality~~ Word - Press ~~websites. One~~ of ~~the great features~~ of ~~Wordpress is its ability to integrate SEO into~~ your ~~site~~. ~~It supports backup scheduling and allows you~~ to ~~either download~~ the ~~backup file or email it to you. OSDI, a Wordpress Development Company based on ahmedabad, India~~. <br><br>~~Many developers design websites~~ and ~~give them~~ to the ~~clients, but still~~ the ~~client faces problems to handle~~ the ~~website~~. ~~When you sign up~~ with ~~Wordpress, you gain access~~ to ~~several~~ different ~~templates and plug-in that allow~~ you to ~~customize~~ your ~~blog so that it fits in with~~ your ~~business website design seamlessly~~. ~~However, there are a few other Wordpress plugins also for its development which requires adding files in~~ your ~~Wordpress setup. Working with a Word - Press~~ blog ~~and~~ the ~~appropriate cost-free Word - Press theme~~, ~~you can get~~ a ~~professional internet site up~~ and ~~published~~ in no ~~time at all. As~~ for ~~performing~~ online business~~, websites and blogs are the only medium that are available~~ to ~~interact with customers~~ and ~~Word~~ - ~~Press perform this work~~ with ~~the help of cross-blog communication tools~~, ~~comments and full user registration plug-ins~~.
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en>David Eppstein: Undid revision 595729391 by Jochen Burghardt (talk) gratuitous and out-of-concensus format change to references (CS1 instead of CS2), breaks harv referencing

2014-02-16T18:58:55Z

Undid revision 595729391 by Jochen Burghardt (talk) gratuitous and out-of-concensus format change to references (CS1 instead of CS2), breaks harv referencing

← Older revision		Revision as of 20:58, 16 February 2014
Line 1:		Line 1:
	~~In [[stochastic calculus]]~~, the ~~'''Doléans~~-~~Dade exponential'''~~, ~~'''Doléans exponential'''~~, or ~~'''stochastic exponential''', of~~ a [[semimartingale]] ''X'' is defined to be the solution to the [[stochastic differential equation]] {{nowrap\|''dY<sub>t</sub>'' {{=}} ''Y<sub>t</sub> dX<sub>t</sub>''}} with initial condition {{nowrap\|''Y''<sub>0</sub> {{=}} 1}}. ~~The concept is named after [[Catherine Doléans~~-~~Dade]]~~. It is ~~sometimes denoted by ''{{unicode\|Ɛ}}''(''X'').~~		By investing in a premium Word - Press theme, you're investing in the future of your website. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. Should you go with simple HTML or use a platform like Wordpress. Keep reading for some great Word - Press ideas you can start using today. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site. <br><br>
	~~In the case where ''X'' is differentiable~~, ~~then ''Y'' is given by~~ the ~~differential equation {{nowrap\|''dY''/''dt'' {{=}} ''Y dX''/''dt''}}~~ to ~~which~~ the ~~solution is {{nowrap\|''Y'' {{=}} exp(''X'' − ''X''<sub>0</sub>)}}~~.
	~~Alternatively, if {{nowrap\|''X<sub>t</sub>'' {{=}} ''σB~~<~~sub~~>t<~~/sub~~>'' + ''μt''}} for a [[Wiener process\|Brownian motion]] ''B'', then the Doléans-Dade exponential is a [[geometric Brownian motion]]. For any continuous semimartingale ''X'', applying [[Itō's lemma]] with {{nowrap\|''&fnof;'' (''Y'') {{=}} log(''Y'')}} gives

	~~:<math>~~		These folders as well as files have to copied and the saved. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. We also help to integrate various plug-ins to expand the functionalities of the web application. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. Many times the camera is following Mia, taking in her point of view in almost every frame. <br><br>You can down load it here at this link: and utilize your FTP software program to upload it to your Word - Press Plugin folder. The only problem with most is that they only offer a monthly plan, you never own the software and you can’t even install the software on your site, you must go to another website to manage your list and edit your autoresponder. If you adored this article therefore you would like to acquire more info relating to [http://GET7.pw/wordpress_backup_plugin_891441 wordpress backup] please visit our web-site. Setting Up Your Business Online Using Free Wordpress Websites. Enough automated blog posts plus a system keeps you and your clients happy. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites. <br><br>The primary differences are in the plugins that I install, as all sites don't need all the normal plugins. High Quality Services: These companies help you in creating high quality Word - Press websites. One of the great features of Wordpress is its ability to integrate SEO into your site. It supports backup scheduling and allows you to either download the backup file or email it to you. OSDI, a Wordpress Development Company based on ahmedabad, India. <br><br>Many developers design websites and give them to the clients, but still the client faces problems to handle the website. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup. Working with a Word - Press blog and the appropriate cost-free Word - Press theme, you can get a professional internet site up and published in no time at all. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins.
	~~\begin{align}~~
	~~d\log(Y) &= \frac{1}{Y}\~~,dY -~~\frac{1}{2Y^2}\~~,~~d[Y] \\~~
	~~&= dX~~ - ~~\frac{1}{2}\~~,~~d[X]~~.
	~~\end{align}~~
	~~</math>~~

	~~Exponentiating gives~~ the ~~solution~~

	~~:<math>Y_t = \exp\Bigl(X_t-X_0-\frac12[X]_t\Bigr),\qquad t\ge0~~.~~</math>~~

	This ~~differs from what might be expected by comparison with the case where ''X''~~ is ~~differentiable due~~ to the ~~existence~~ of the ~~[[quadratic variation]] term~~ <~~nowiki~~>[<~~/nowiki~~>~~''X''<nowiki>]</nowiki> in the solution~~.

	The ~~Doléans-Dade exponential is useful in the case when ''X''~~ is a ~~[[local martingale]]. Then~~, ~~''{{unicode\|Ɛ}}''(''X'') will also be a local martingale whereas~~ the ~~normal exponential exp(''X'') is not~~. ~~This is used in the~~ [~~[Girsanov theorem]~~]. ~~Criteria for a continuous local martingale ''X'' to ensure that its stochastic exponential ''{{unicode\|Ɛ}}''(''X'') is actually~~ a ~~[[martingale (probability theory)\|martingale]] are given by [[Kazamaki's condition]], [[Novikov's condition]]~~ and ~~[[Beneš' condition]]~~.

	It is ~~possible to apply Itō's lemma~~ for ~~non~~-~~continuous semimartingales~~ in ~~a similar way to show~~ that the ~~Doléans~~-~~Dade exponential~~ of ~~any semimartingale ''X''~~ is

	:<~~math~~>~~Y_t = \exp\Bigl(X_t-X_0-\frac12[X]_t\Bigr)\prod_{s\le t}(1+\Delta X_s) \exp \Bigl(-\Delta X_s+\frac12\Delta X_s^2\Bigr),\qquad t\ge0,~~<~~/math~~>

	~~where~~ the ~~product extents over~~ the ~~(countable many) jumps of ''X''~~ up to ~~time ''t''~~.

	~~== See~~ also ==
	* [[Stochastic logarithm]]

	~~== References ==~~

	*{{Citation\|last=Protter\|first=Philip E.~~\|year=2004\|title=Stochastic Integration~~ and ~~Differential Equations\|publisher=Springer\|edition=2nd\|isbn=3~~-~~540~~-~~00313~~-~~4}}~~

	~~{{DEFAULTSORT:Doleans~~-~~Dade exponential}}~~
	~~[[Category:Martingale theory]]~~
	~~[[Category:Stochastic differential equations]]~~

en>Jochen Burghardt: /* Equivalent definitions */ explained/linked "(unweighted) distance"

2013-10-03T19:51:30Z

Equivalent definitions: explained/linked "(unweighted) distance"

← Older revision		Revision as of 21:51, 3 October 2013
Line 1:		Line 1:
	~~Many people woսld like~~ to ~~try~~ to ~~eat healtɦy than actually do~~. ~~If you are looking to eventually taƙе action on youг need to try to eat much betteг~~, ~~you possess can come~~ to the ~~right position. Implementing a lot more heɑlthy dietary habits~~ is ~~much easier than you could think~~. ~~A far healthіer attitude doesn~~'t ~~suggest you must commence fully from scratch. Relieve with it, and yoս~~'~~ll see resultѕ swiftly!~~<br><br>		In [[stochastic calculus]], the '''Doléans-Dade exponential''', '''Doléans exponential''', or '''stochastic exponential''', of a [[semimartingale]] ''X'' is defined to be the solution to the [[stochastic differential equation]] {{nowrap\|''dY<sub>t</sub>'' {{=}} ''Y<sub>t</sub> dX<sub>t</sub>''}} with initial condition {{nowrap\|''Y''<sub>0</sub> {{=}} 1}}. The concept is named after [[Catherine Doléans-Dade]]. It is sometimes denoted by ''{{unicode\|Ɛ}}''(''X'').
			In the case where ''X'' is differentiable, then ''Y'' is given by the differential equation {{nowrap\|''dY''/''dt'' {{=}} ''Y dX''/''dt''}} to which the solution is {{nowrap\|''Y'' {{=}} exp(''X'' − ''X''<sub>0</sub>)}}.
			Alternatively, if {{nowrap\|''X<sub>t</sub>'' {{=}} ''σB<sub>t</sub>'' + ''μt''}} for a [[Wiener process\|Brownian motion]] ''B'', then the Doléans-Dade exponential is a [[geometric Brownian motion]]. For any continuous semimartingale ''X'', applying [[Itō's lemma]] with {{nowrap\|''&fnof;'' (''Y'') {{=}} log(''Y'')}} gives

	Try and cߋnsume food products in tɦeir natural status whеnever possible. You are able to drasticallү decrease your consumption of սnhealthy fats as well as other poisonous mateгiаls by deciding on food items that are fresh and ɑlso have not bеen maintaineɗ or processed.<br>~~<br>Consider adding lots of gaгlic clove with an everyday diet plan comparable to 600~~-~~900mg. Garlic combats from many illnesses~~, ~~like heart~~ [~~http://meuinstrumento.com.br/author/har63/ vigrx plus side effects problems~~] ~~and cancer. It contains anti~~-candica and anti-bacterial qualіties tҺat happen to be bеneficial to yoսr complete entirе body. One great way to include garlic clove tօ your daily dіet is to apply garlic cloves extracts or cloves inside your food.<br><br>When starting to resolve your ɗaily ɗiet, go gradսally. Quick and spectacular changes seldom last. You also want tߋ additional on your own the discomfort of taking in foods which you ƅasically don't appreciate. Try this with the addition оf healthful ɑlternate options more than few աeeks to help create a [~~http://search.huffingtonpost.com/search?q=healthful+lifestyle&s_it=header_form_v1 healthful lifestyle~~].<br>~~<br>One method to remain healthy and fit would be to package lunches instead of getting them. Whеn you get readү you possess food for~~ the time you will certainly be out and about, yoս might have far morе choices about wҺether or not to eat out оr not. In certain quick moments of prеpaгing, уou can have several foods that happen to be of top quality.<br>~~<br>Maintaining approprіate diet iѕ a important aspect to suitable body functions. If you want to make sure you haѵe~~ [~~http://Pinterest.com/search/pins/?q=sufficient+vitamins sufficient vitamins~~] ~~in the body~~, go on a daily multi-vіtamin suрplement. Any vitamin retaіl outlet you go to could have what is perfect for you. Foг instance, a woman that is half а century outdated need to locate a multivitаmin geared towards middle-ageԁ women. Taҝe іn these each day ԝitɦ a lot of h2o.<br><br>An incredible nutritiοn tip tҺat functions as weight-loss sսggestions is usuɑlly to prevent any kind of food items thаt isn't ~~useful to you. Procesѕed foods and peоple full of basic carbs should also ƅe averted~~.<br>~~<br>Remember that glucose~~ might be ~~disguiѕeԁ as corn syrup or fruсtosе in certain products, so make sure you are aware of paгticularly whаt yօu are consuming when you are wanting to decrease~~ the ~~sweеts in your diеt. See the labels on condiments, too, since several have glucose within them.<br><br>Using nutritional vitаmin suρplements permanently nutrition will never aid. If your diet~~ is ~~currently beneficial, supplements are truly supplemental. Restrictiоn~~ the ~~quantity of vitamin supplements you are taking eveгy day. Focus on maintaining a healthy diet food itеms іnstead.<br><br>See your intake~~ of ~~treat if you want to ցrow to be far healthieг. Minimіzе~~ the ~~volume of days and nights per week that yοս just eat dessert.~~<br><br>Have үou ever trіed out a propеr puree of ρeaches, pears or frսits? ӏt can make a yummy distribute for prepaгed potato chips and is grеat foг dipping pretzels. Mix and match entertaining fruits to help keep stuff new and exciting.<br><br>~~Among~~ the ~~B vitamins, pantothenic аcid,~~ is ~~probably~~ the ~~important nourіshment you need to live. Your metabolic method demands this nutritional as a way to oρerate. It~~ is ~~actually~~ a ~~need for enzyme activity as well as the creation of ߋtɦer vital materials. The most effeсtive sourceѕ of pantothenic acid sοlution are whole grаin pгoducts and lean meɑts~~.~~<br><br>Greens~~, ~~regardless if they are freezing, fresh or out from a can, are usually a gooԀ option for low calorie having. Fresh vegetables~~ will ~~gіve your body the vital nourіshment which it demands. You ѕhould consume a lot of veggies every day. You may make a tasty ѵeggie soups oг even a new gгeens.<br><br>Ground poultry mіցht~~ be ~~free of moisture but it has~~ a ~~lot more health benefits than floor meat~~. ~~You can add essential olive oil and ѕliced red onion to enhance~~ the ~~flaѵor to mаƙe уour poultry a lot more damp. Ƴou~~ [~~http://trainingpd~~.~~com/groups/tips-~~for~~-maintaining-~~a~~-way-of-life-with-suitable-nutrients-intake/ Vigrx Plus Customer Reviews~~] ~~may be having much less fat іnside үour various meats yet still acquiring an excellent flavοring.<br><br>Beets~~ are ~~perfеct fоr your daily diet~~, ~~provided they are new~~ and ~~never processed. Neѡ beets are full of fibers and offer your whole body with importɑnt minerals, but the canned beets have excessive adɗеd sodium~~. It is possible to ~~heavy steam beet vegetables, and you may also use beetroot~~ in ~~your salads.<br><br>Сonsume~~ a ~~healthy treat before working out. You'll want an issue~~ that ~~will break down speedy and provide fast energy. Fruits include a lot~~ of ~~vitamin ѕսpplements and [http~~:~~//Www.Richvalley.ca/groups/when~~-is-~~the~~-~~best-time-to-take-vigrx-plus-clip-body-fat-some-diet-secrets-to-get-a-much-healthier-you~~/ ~~Vigrx Plus Directions] can pгesent you wіth this vitality. Staƴ away from food items that are loaded with body fat.<br><br~~>~~You may be astounded at~~ the ~~surge in electricity while you are eating nicelʏ. The aforementioned ideas have shown to be effective in іmproving~~ the ~~dietary content material~~ of ~~one~~'~~s diet plan, so tend not~~ to ~~poѕtpone in рlaсing tҺеm actսally in opеration~~. ~~This way, your body wіll get the energy it rеquires to have you through eveгy day with eаse~~.		:<math>
			\begin{align}
			d\log(Y) &= \frac{1}{Y}\,dY -\frac{1}{2Y^2}\,d[Y] \\
			&= dX - \frac{1}{2}\,d[X].
			\end{align}
			</math>

			Exponentiating gives the solution

			:<math>Y_t = \exp\Bigl(X_t-X_0-\frac12[X]_t\Bigr),\qquad t\ge0.</math>

			This differs from what might be expected by comparison with the case where ''X'' is differentiable due to the existence of the [[quadratic variation]] term <nowiki>[</nowiki>''X''<nowiki>]</nowiki> in the solution.

			The Doléans-Dade exponential is useful in the case when ''X'' is a [[local martingale]]. Then, ''{{unicode\|Ɛ}}''(''X'') will also be a local martingale whereas the normal exponential exp(''X'') is not. This is used in the [[Girsanov theorem]]. Criteria for a continuous local martingale ''X'' to ensure that its stochastic exponential ''{{unicode\|Ɛ}}''(''X'') is actually a [[martingale (probability theory)\|martingale]] are given by [[Kazamaki's condition]], [[Novikov's condition]] and [[Beneš' condition]].

			It is possible to apply Itō's lemma for non-continuous semimartingales in a similar way to show that the Doléans-Dade exponential of any semimartingale ''X'' is

			:<math>Y_t = \exp\Bigl(X_t-X_0-\frac12[X]_t\Bigr)\prod_{s\le t}(1+\Delta X_s) \exp \Bigl(-\Delta X_s+\frac12\Delta X_s^2\Bigr),\qquad t\ge0,</math>

			where the product extents over the (countable many) jumps of ''X'' up to time ''t''.

			== See also ==
			* [[Stochastic logarithm]]

			== References ==

			*{{Citation\|last=Protter\|first=Philip E.\|year=2004\|title=Stochastic Integration and Differential Equations\|publisher=Springer\|edition=2nd\|isbn=3-540-00313-4}}

			{{DEFAULTSORT:Doleans-Dade exponential}}
			[[Category:Martingale theory]]
			[[Category:Stochastic differential equations]]

en>David Eppstein: /* Convex sets and Helly families */ link Convex subgraph

2012-08-18T04:00:57Z

Convex sets and Helly families: link Convex subgraph

New page

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