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000755089 019__ $$a948632329
000755089 020__ $$a9783319310893$$q(electronic book)
000755089 020__ $$a3319310895$$q(electronic book)
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000755089 0247_ $$a10.1007/978-3-319-31089-3$$2doi
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000755089 08204 $$a519.2/33$$223
000755089 1001_ $$aLe Gall, J. F.$$q(Jean-François),$$eauthor.
000755089 24510 $$aBrownian motion, martingales, and stochastic calculus$$h[electronic resource] /$$cJean-François Le Gall.
000755089 264_1 $$aSwitzerland :$$bSpringer,$$c2016.
000755089 300__ $$a1 online resource (xi, 273 pages) :$$billustrations.
000755089 336__ $$atext$$btxt$$2rdacontent
000755089 337__ $$acomputer$$bc$$2rdamedia
000755089 338__ $$aonline resource$$bcr$$2rdacarrier
000755089 4901_ $$aGraduate texts in mathematics,$$x0072-5285 ;$$v274
000755089 504__ $$aIncludes bibliographical references and index.
000755089 5050_ $$aGaussian variables and Gaussian processes -- Brownian motion -- Filtrations and martingales -- Continuous semimartingales -- Stochastic integration -- General theory of Markov processes -- Brownian motion and partial differential equations -- Stochastic differential equations -- Local times -- The monotone class lemma -- Discrete martingales -- References.
000755089 506__ $$aAccess limited to authorized users.
000755089 520__ $$aThis book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô?s formula, the optional stopping theorem and Girsanov?s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
000755089 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed May 4, 2016).
000755089 650_0 $$aBrownian motion processes.
000755089 650_0 $$aMartingales (Mathematics)
000755089 77608 $$iPrint version:$$z9783319310886
000755089 830_0 $$aGraduate texts in mathematics ;$$v274.
000755089 852__ $$bebk
000755089 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-31089-3$$zOnline Access$$91397441.1
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