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008			160527s2016 sz s 000 0 eng d
010			_a2016938909
019			_a939531849
020			_a3319310887 _q(print)
020			_a9783319310886 _q(print)
020			_z3319310895 _q(eBook)
020			_z9783319310893 _q(eBook)
024	3		_a9783319310886
035			_a(OCoLC)950732866
040			_aINT _beng _erda _cINT _dINT _dOHX _dHCD _dYDXCP _dOCLCF _dEQO _dNHM _dCUY _dBTCTA _dBDX _dMUU _dS3O _dOCLCQ
041	1		_aeng _hfre
050		4	_aQA274.75 _b.L4413 2016x
100	1		_aLe Gall, J. F. _q(Jean-Fran©ʹois), _eauthor.
240	1	0	_aMouvement brownien, martingales et calcul stochastique. _lEnglish
245	1	0	_aBrownian motion, martingales, and stochastic calculus / _cJean-Franois Le Gall.
264		1	_aSwitzerland : _bSpringer, _c[2016]
300			_axiii, 273 pages : _billustrations ; _c24 cm.
336			_atext _2rdacontent
337			_acomputer _2rdamedia
338			_aonline resource _2rdacarrier
490	1		_aGraduate texts in mathematics, _x0072-5285 ; _v274
500			_aTranslated from the French edition published: Berlin: Springer, 2013.
504			_aIncludes bibliographical references and index.
505	0		_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 It©þ'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 It©þ, 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.
650		0	_aBrownian motion processes.
650		0	_aCalculus.
650		0	_aMartingales (Mathematics)
650		0	_aStochastic analysis.
830		0	_aGraduate texts in mathematics ; _v274.
856			_uhttps://drive.google.com/file/d/1NAOCb17rI5XFPDRb3QLMVmk7cojCbbDY/view?usp=sharing
999			_c9389 _d9389