000			02685nam a22002535i 4500
008			160414s2016 nyu 000 0 eng
020			_a9783319310886 (HB)
041			_aeng
080			_a519.216 _bLE
100			_aLe Gall, Jean-Francois
245	0	0	_aBrownian motion, martingales, and stochastic calculus
260			_aSwitzerland _bSpringer _c2016
300			_axiii, 273p.
490			_aGraduate Texts in Mathematics _v274
504			_aIncludes References
505			_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
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
546			_a Translated from the French edition published: Berlin: Springer, 2013
650			_aStochastic analysis _vcalculus
650			_aBrownian motion
650			_aMartingales
690			_aMathematics
942			_cBK
999			_c60628 _d60628