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- Stochastic_calculus abstract "Stochastic calculus is a branch of mathematics that operates on stochastic processes. 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 therefore does 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 Rn.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.".
- Stochastic_calculus wikiPageExternalLink 0712.3908v2.pdf.
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- Stochastic_calculus wikiPageWikiLink Albert_Einstein.
- Stochastic_calculus wikiPageWikiLink Black–Scholes_model.
- Stochastic_calculus wikiPageWikiLink Brownian_motion.
- Stochastic_calculus wikiPageWikiLink Category:Integral_calculus.
- Stochastic_calculus wikiPageWikiLink Category:Mathematical_finance.
- Stochastic_calculus wikiPageWikiLink Category:Stochastic_calculus.
- Stochastic_calculus wikiPageWikiLink Chain_rule.
- Stochastic_calculus wikiPageWikiLink Diffusion.
- Stochastic_calculus wikiPageWikiLink Dominated_convergence_theorem.
- Stochastic_calculus wikiPageWikiLink Economics.
- Stochastic_calculus wikiPageWikiLink Financial_mathematics.
- Stochastic_calculus wikiPageWikiLink Geometric_Brownian_motion.
- Stochastic_calculus wikiPageWikiLink Integral.
- Stochastic_calculus wikiPageWikiLink Integrals.
- Stochastic_calculus wikiPageWikiLink Itxc3xb4s_lemma.
- Stochastic_calculus wikiPageWikiLink Itxc5x8ds_lemma.
- Stochastic_calculus wikiPageWikiLink Itô_calculus.
- Stochastic_calculus wikiPageWikiLink Itō_calculus.
- Stochastic_calculus wikiPageWikiLink Itō_integral.
- Stochastic_calculus wikiPageWikiLink Louis_Bachelier.
- Stochastic_calculus wikiPageWikiLink Malliavin_calculus.
- Stochastic_calculus wikiPageWikiLink Mathematical_finance.
- Stochastic_calculus wikiPageWikiLink Mathematics.
- Stochastic_calculus wikiPageWikiLink Norbert_Wiener.
- Stochastic_calculus wikiPageWikiLink Quadratic_variation.
- Stochastic_calculus wikiPageWikiLink Quantitative_finance.
- Stochastic_calculus wikiPageWikiLink Semimartingale.
- Stochastic_calculus wikiPageWikiLink Stochastic_differential_equation.
- Stochastic_calculus wikiPageWikiLink Stochastic_differential_equations.
- Stochastic_calculus wikiPageWikiLink Stochastic_process.
- Stochastic_calculus wikiPageWikiLink Stratonovich_integral.
- Stochastic_calculus wikiPageWikiLink Wiener_process.
- Stochastic_calculus wikiPageWikiLinkText "Itō integral".
- Stochastic_calculus wikiPageWikiLinkText "Random Calculus".
- Stochastic_calculus wikiPageWikiLinkText "Stochastic calculus".
- Stochastic_calculus wikiPageWikiLinkText "Stochastic models".
- Stochastic_calculus wikiPageWikiLinkText "stochastic calculus".
- Stochastic_calculus wikiPageWikiLinkText "stochastic differential and integral calculus".
- Stochastic_calculus wikiPageWikiLinkText "stochastic integral equations".
- Stochastic_calculus wikiPageWikiLinkText "stochastic integration".
- Stochastic_calculus wikiPageWikiLinkText "stochastic models".
- Stochastic_calculus wikiPageWikiLinkText "stochastic".
- Stochastic_calculus hasPhotoCollection Stochastic_calculus.
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- Stochastic_calculus subject Category:Integral_calculus.
- Stochastic_calculus subject Category:Mathematical_finance.
- Stochastic_calculus subject Category:Stochastic_calculus.
- Stochastic_calculus hypernym Branch.
- Stochastic_calculus type Article.
- Stochastic_calculus type Organisation.
- Stochastic_calculus type Article.
- Stochastic_calculus type Field.
- Stochastic_calculus type Occupation.
- Stochastic_calculus type Process.
- Stochastic_calculus comment "Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes.".
- Stochastic_calculus label "Stochastic calculus".
- Stochastic_calculus sameAs حساب_التفاضل_والتكامل_العشوائي.
- Stochastic_calculus sameAs Stochastische_Analysis.
- Stochastic_calculus sameAs Calcul_stochastique.
- Stochastic_calculus sameAs Cálculo_estocástico.
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- Stochastic_calculus sameAs Q1308570.
- Stochastic_calculus sameAs Q1308570.
- Stochastic_calculus sameAs 随机分析.
- Stochastic_calculus wasDerivedFrom Stochastic_calculus?oldid=678317519.
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