Economic equilibrium - Revision history

112.208.173.63: /* Example: The competitive equilibrium. */

2014-07-01T12:57:50Z

Example: The competitive equilibrium.

← Older revision		Revision as of 14:57, 1 July 2014
Line 1:		Line 1:
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2602:306:CDD1:2120:3C5D:130:217E:8F51: /* Solving for the competitive equilibrium price */

2014-02-19T06:18:37Z

Solving for the competitive equilibrium price

← Older revision		Revision as of 08:18, 19 February 2014
Line 1:		Line 1:
	~~{{Calculus \|Specialized}}~~		This Halloween, make a hot tradition. Instead of it being a day, or days, of indulging in the favorite sugary treats, create it a day for creating healthy resolutions.<br><br>So when [http://safedietplansforwomen.com/bmr-calculator bmr calculator] this is happening to we and you don't desire to be apple shaped, what are you able to do regarding it. First, consider your diet. Cut out processed foods and saturated fat. Items like butter, cakes, biscuits, full fat milk, white bread, prepared created food.<br><br>There are on-line websites which may allow you to estimate the basal metabolic rate. Some include a age in the calculation, others do not. Some just utilize a weight, gender and exercise level. You will find that the results can fluctuate generally. From this calculation, you are able to then estimate the daily calorie needs from carbs, proteins and fats. For many folks on a fat reduction diet, calories are limited from 1200 to 1500 a day.<br><br>While supplementing with pyruvate, we needn't go on an overly stringent diet. But, when you eat anything we need without respect to calories or fat consumption or without exercising, you'll only receive fatter. Your right bet is to follow a moderate, well-balanced however low-fat diet plus exercise program that decreases your calories by no over 500 a day, either by exercise, a slight reduction inside food, or perhaps a mixture of the two. At www.ShopPharmacyCounter.com you sell right fat loss supplements. Suppose we need an intake of 2,200 calories a day to keep the weight. To lose fat, you'll need to cut 500 calories daily, for a caloric consumption of 1,700 calories a day.<br><br>So how do you understand how many calories you want? There is no magic amount which fits everybody. Many factors have a role in determining what the appropriate amount is for you. Some of these factors include age, current fat, activity level, height, plus bmr.<br><br>3) Eat gradually - When we eat gradually, the process of chewing plus mixing foods inside our mouth with saliva is the initial step in digestion. The more you chew the foods, the less function is required to digest them. For persons who are constantly experiencing bloating, stomach pain or heartburn after eating, they are eating too fast plus are causing indigestion. The additional advantage of eating gradually is to prevent over eating. By eating slowing, you allow the belly to signal the mind whenever you have consumed enough before you have consumed too much. For folks who wish To eat less, eating slowly is many effective.<br><br>In summary, you will certainly do quite a bit to better our metabolism. Lifestyle change and consistent frequent exercise, all may enhance metabolic rate.

	~~'''Stochastic calculus''' is~~ a ~~branch~~ of ~~[[mathematics]] that operates on [[stochastic process]]es. It allows~~ a ~~consistent theory~~ of ~~integration to be defined~~ for [~~[integrals~~]~~] of stochastic processes with respect to stochastic processes. It~~ is ~~used~~ to ~~model systems that behave randomly.~~

	~~The best-known stochastic process~~ to ~~which stochastic calculus is applied is the [[Wiener process]] (named in honor of [[Norbert Wiener]])~~, ~~which is used for modeling [[Brownian motion]] as described by [[Louis Bachelier]] in 1900 and by [[Albert Einstein]] in 1905 and other physical [[diffusion]] processes in space of particles subject~~ to ~~random forces~~. ~~Since the 1970s~~, ~~the Wiener process has been widely applied in [[financial mathematics]]~~ and ~~[[economics]]~~ to ~~model~~ the ~~evolution~~ in ~~time of stock prices and bond interest rates~~.

	~~The main flavours of stochastic calculus are the [[Itō calculus]]~~ and ~~its variational relative the [[Malliavin calculus]]~~. ~~For technical reasons~~ the Itō integral is the most useful for general classes of processes but the related [[Stratonovich integral]] is frequently useful in problem formulation (particularly in engineering disciplines.) The Stratonovich integral can ~~readily be expressed in terms of the Itō integral~~. ~~The main benefit of~~ the ~~Stratonovich integral is that it obeys the usual [[chain rule]]~~ and ~~does therefore not require [[Itō's lemma]]~~. ~~This enables problems~~ to ~~be expressed in~~ a ~~coordinate system invariant form, which is invaluable when developing stochastic calculus on manifolds other than '''R'''~~<~~sup~~>~~''n''~~<~~/sup~~>.
	~~The [[dominated convergence theorem]] does not hold for the Stratonovich integral~~, ~~consequently it~~ is ~~very difficult~~ to ~~prove results without re~~-~~expressing~~ the ~~integrals in Itō form~~.

	~~== Itō integral ==~~
	~~{{main\|Itō calculus}}~~

	~~The [[Itō integral]] is central~~ to the ~~study of stochastic calculus~~. ~~The integral <math>\int H\~~,~~dX</math> is defined~~ for a ~~[[semimartingale]] ''X'' and locally bounded '''predictable''' process ''H''. {{Citation needed\|date=August 2011}}~~

	~~== Stratonovich integral ==~~
	~~{{main\|Stratonovich integral}}~~

	~~The Stratonovich integral~~ of a ~~[[semimartingale]]~~ <~~math~~>X<~~/math~~> ~~against another [[semimartingale]] ''Y'' can be defined~~ in ~~terms~~ of ~~the Itō integral as~~

	~~:<math> \int_0^t X_{s-} \circ d Y_s : = \int_0^t X_{s-} d Y_s + \frac{1}{2} \left [ X~~, ~~Y\right]_t^c~~,~~</math>~~

	~~where [''X''~~,~~ ''Y'']<sub>''t''~~<~~/sub~~><~~sup~~>~~''c''</sup> denotes~~ the ~~[[Quadratic variation\|quadratic covariation]]~~ of the ~~continuous parts of ''X''~~
	~~and ''Y''~~. The ~~alternative notation~~

	~~:<math> \int_0^t X_s \~~, ~~\partial Y_s </math>~~

	is ~~also used~~ to ~~denote the Stratonovich integral~~.

	~~== Applications ==~~

	~~An important application~~ of ~~stochastic calculus~~ is ~~in [[quantitative finance]], in which asset prices are often assumed~~ to ~~follow [[stochastic differential equations]]~~. In the ~~[[Black-Scholes model]], prices are assumed~~ to ~~follow~~ the ~~[[geometric Brownian motion]]~~.

	~~{{No footnotes\|date=August 2011}}~~

	~~== References ==~~
	* Fima C Klebaner, ~~2012~~, ~~Introduction~~ to ~~Stochastic Calculus with Application (3rd Edition)~~. ~~World Scientific Publishing~~, ~~ISBN 9781848168312~~
	* {{cite doi\|10.1007/s10959-007-0140-8}} [http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3908v2.~~pdf Preprint]~~

	~~[[Category:Stochastic calculus\| ]]~~
	~~[[Category:Mathematical finance]]~~
	~~[[Category:Integral calculus]]~~

en>Materialscientist: Reverted 1 edit by 117.193.219.130 identified as test/vandalism using STiki

2014-01-14T12:33:37Z

Reverted 1 edit by 117.193.219.130 identified as test/vandalism using STiki

← Older revision		Revision as of 14:33, 14 January 2014
Line 1:		Line 1:
	~~They contact me Emilia~~. ~~He utilized~~ to be ~~unemployed but now he~~ is ~~a meter reader~~. ~~One~~ of the ~~things he loves~~ most is ~~ice skating but he~~ is ~~struggling~~ to ~~discover time~~ for it. ~~Years~~ in the ~~past we moved to Puerto Rico~~ and ~~my family members enjoys it~~.<br><br>~~Take a look at my web~~-~~site;~~ [http://~~snuda~~.org/xe/~~?document_srl=94520 over the counter std test~~]		{{Calculus \|Specialized}}

			'''Stochastic calculus''' is a branch of [[mathematics]] that operates on [[stochastic process]]es. It allows a consistent theory of integration to be defined for [[integrals]] of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly.

			The best-known stochastic process to which stochastic calculus is applied is the [[Wiener process]] (named in honor of [[Norbert Wiener]]), which is used for modeling [[Brownian motion]] as described by [[Louis Bachelier]] in 1900 and by [[Albert Einstein]] in 1905 and other physical [[diffusion]] processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in [[financial mathematics]] and [[economics]] to model the evolution in time of stock prices and bond interest rates.

			The main flavours of stochastic calculus are the [[Itō calculus]] and its variational relative the [[Malliavin calculus]]. For technical reasons the Itō integral is the most useful for general classes of processes but the related [[Stratonovich integral]] is frequently useful in problem formulation (particularly in engineering disciplines.) The Stratonovich integral can readily be expressed in terms of the Itō integral. The main benefit of the Stratonovich integral is that it obeys the usual [[chain rule]] and does therefore not require [[Itō's lemma]]. This enables problems to be expressed in a coordinate system invariant form, which is invaluable when developing stochastic calculus on manifolds other than '''R'''<sup>''n''</sup>.
			The [[dominated convergence theorem]] does not hold for the Stratonovich integral, consequently it is very difficult to prove results without re-expressing the integrals in Itō form.

			== Itō integral ==
			{{main\|Itō calculus}}

			The [[Itō integral]] is central to the study of stochastic calculus. The integral <math>\int H\,dX</math> is defined for a [[semimartingale]] ''X'' and locally bounded '''predictable''' process ''H''. {{Citation needed\|date=August 2011}}

			== Stratonovich integral ==
			{{main\|Stratonovich integral}}

			The Stratonovich integral of a [[semimartingale]] <math>X</math> against another [[semimartingale]] ''Y'' can be defined in terms of the Itō integral as

			:<math> \int_0^t X_{s-} \circ d Y_s : = \int_0^t X_{s-} d Y_s + \frac{1}{2} \left [ X, Y\right]_t^c,</math>

			where [''X'', ''Y'']<sub>''t''</sub><sup>''c''</sup> denotes the [[Quadratic variation\|quadratic covariation]] of the continuous parts of ''X''
			and ''Y''. The alternative notation

			:<math> \int_0^t X_s \, \partial Y_s </math>

			is also used to denote the Stratonovich integral.

			== Applications ==

			An important application of stochastic calculus is in [[quantitative finance]], in which asset prices are often assumed to follow [[stochastic differential equations]]. In the [[Black-Scholes model]], prices are assumed to follow the [[geometric Brownian motion]].

			{{No footnotes\|date=August 2011}}

			== References ==
			* Fima C Klebaner, 2012, Introduction to Stochastic Calculus with Application (3rd Edition). World Scientific Publishing, ISBN 9781848168312
			* {{cite doi\|10.1007/s10959-007-0140-8}} [http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3908v2.pdf Preprint]

			[[Category:Stochastic calculus\| ]]
			[[Category:Mathematical finance]]
			[[Category:Integral calculus]]

en>SchreiberBike: Repairing links to disambiguation pages - You can help! - Equilibrium

2012-08-29T01:10:46Z

Repairing links to disambiguation pages - You can help! - Equilibrium

New page

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