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LEADER: 03927nam a22005055a 4500
001 014158718-0
005 20141003190840.0
008 130321s2003 gw | o ||0| 0|eng d
020 $a9783662100615
020 $a9783642055607 (ebk.)
020 $a9783662100615
020 $a9783642055607
024 7 $a10.1007/978-3-662-10061-5$2doi
035 $a(Springer)9783662100615
040 $aSpringer
050 4 $aQA273.A1-274.9
050 4 $aQA274-274.9
072 7 $aMAT029000$2bisacsh
072 7 $aPBT$2bicssc
072 7 $aPBWL$2bicssc
082 04 $a519.2$223
100 1 $aProtter, Philip E.,$eauthor.
245 10 $aStochastic Integration and Differential Equations /$cby Philip E. Protter.
250 $aSecond Edition, Version 2.1.
264 1 $aBerlin, Heidelberg :$bSpringer Berlin Heidelberg :$bSpringer,$c2003.
300 $aXIII, 421 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aStochastic Modelling and Applied Probability, Applications of Mathematics,$x0172-4568 ;$v21
505 0 $aI Preliminaries -- II Semimartingales and Stochastic Integrals -- III Semimartingales and Decomposable Processes -- IV General Stochastic Integration and Local Times -- V Stochastic Differential Equations -- VI Expansion of Filtrations -- References.
520 $aIt has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emeryâ¬(tm)s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H 1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
650 20 $aDifferential equations, Partial.
650 10 $aMathematics.
650 0 $aDistribution (Probability theory)
650 0 $aDifferential equations, partial.
650 0 $aEngineering mathematics.
650 0 $aMathematics.
650 24 $aAppl.Mathematics/Computational Methods of Engineering.
650 24 $aProbability Theory and Stochastic Processes.
776 08 $iPrinted edition:$z9783642055607
830 0 $aStochastic Modelling and Applied Probability, Applications of Mathematics ;$v21.
988 $a20140910
906 $0VEN