000			03599nam a22004815i 4500
001			978-1-4614-9587-1
003			DE-He213
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007			cr nn 008mamaa
008			131109s2014 xxu| s |||| 0|eng d
020			_a9781461495871 _9978-1-4614-9587-1
024	7		_a10.1007/978-1-4614-9587-1 _2doi
050		4	_aQA273.A1-274.9
050		4	_aQA274-274.9
072		7	_aPBT _2bicssc
072		7	_aPBWL _2bicssc
072		7	_aMAT029000 _2bisacsh
082	0	4	_a519.2 _223
100	1		_aChung, K.L. _eauthor.
245	1	0	_aIntroduction to Stochastic Integration _h[electronic resource] / _cby K.L. Chung, R.J. Williams.
250			_a2nd ed. 2014.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Birkhäuser, _c2014.
300			_aXVII, 276 p. 10 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics, _x2197-1803
505	0		_a1 Preliminaries -- 2 Definition of the Stochastic Integral -- 3 Extension of the Predictable Integrands -- 4 Quadratic Variation Process -- 5 The Ito Formula -- 6 Applications of the Ito Formula -- 7 Local Time and Tanaka's Formula -- 8 Reflected Brownian Motions -- 9 Generalization Ito Formula, Change of Time and Measure -- 10 Stochastic Differential Equations -- References -- Index.
520			_aA highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.   Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed.   New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use.   This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis.   The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association     An attractive text…written in [a] lean and precise style…eminently readable. Especially pleasant are the care and attention devoted to details… A very fine book. —Mathematical Reviews
650		0	_aMathematics.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
700	1		_aWilliams, R.J. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461495864
830		0	_aModern Birkhäuser Classics, _x2197-1803
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-9587-1
912			_aZDB-2-SMA
999			_c92399 _d92399