LEADER 04260nam 22006015 450 001 9910300147803321 005 20250718152028.0 010 $a1-4614-9587-3 024 7 $a10.1007/978-1-4614-9587-1 035 $a(CKB)3710000000078559 035 $a(Springer)9781461495871 035 $a(MH)013879511-8 035 $a(SSID)ssj0001067595 035 $a(PQKBManifestationID)11696848 035 $a(PQKBTitleCode)TC0001067595 035 $a(PQKBWorkID)11093479 035 $a(PQKB)11047623 035 $a(DE-He213)978-1-4614-9587-1 035 $a(MiAaPQ)EBC3091906 035 $a(PPN)176101624 035 $a(EXLCZ)993710000000078559 100 $a20131109d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Stochastic Integration /$fby K.L. Chung, R.J. Williams 205 $a2nd ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XVII, 276 p. 10 illus.)$conline resource 225 1 $aModern Birkhäuser Classics,$x2197-1811 300 $a"Originally published in the series Probability and its applications."--Title page verso. 311 08$a1-4614-9586-5 320 $aIncludes bibliographical references (pages 265-272) and index. 327 $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. 330 $aA highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.   Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô?s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman?Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed.   New to the second edition are a discussion of the Cameron?Martin?Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use.   This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis.   The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. ?Journal of the American Statistical Association     An attractive text?written in [a] lean and precise style?eminently readable. Especially pleasant are the care and attention devoted to details? A very fine book. ?Mathematical Reviews  . 410 0$aModern Birkhäuser Classics,$x2197-1811 606 $aProbabilities 606 $aProbability Theory 615 0$aProbabilities. 615 14$aProbability Theory. 676 $a519.2/2 700 $aChung$b Kai Lai$f1917-2009$4aut$4http://id.loc.gov/vocabulary/relators/aut$012286 702 $aWilliams$b R. J$g(Ruth J.),$f1955-$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300147803321 996 $aIntroduction to stochastic integration$9375877 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress