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100   $a20160428d2016      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aBrownian Motion, Martingales, and Stochastic Calculus $b[electronic resource] /$fby Jean-François Le Gall
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XIII, 273 p. 5 illus., 1 illus. in color.) 
225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v274
300   $aIncludes Index.
311   $a3-319-31088-7 
327   $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.
330   $aThis book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô?s formula, the optional stopping theorem and Girsanov?s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
410  0$aGraduate Texts in Mathematics,$x0072-5285 ;$v274
606   $aProbabilities
606   $aEconomics, Mathematical 
606   $aMeasure theory
606   $aMathematical models
606   $aSystem theory
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068
606   $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070
615  0$aProbabilities.
615  0$aEconomics, Mathematical .
615  0$aMeasure theory.
615  0$aMathematical models.
615  0$aSystem theory.
615 14$aProbability Theory and Stochastic Processes.
615 24$aQuantitative Finance.
615 24$aMeasure and Integration.
615 24$aMathematical Modeling and Industrial Mathematics.
615 24$aSystems Theory, Control.
676   $a519.23
700   $aLe Gall$b Jean-François$4aut$4http://id.loc.gov/vocabulary/relators/aut$0348889
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254069803321
996   $aBrownian motion, martingales, and stochastic calculus$91523199
997   $aUNINA