000			02708 a2200253 4500
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020			_a9783642055607
040			_cIIT Kanpur
041			_aeng
082			_a519.2 _bP946s2
100			_aProtter, Philip E.
245			_aStochastic integration and differential equations _cPhilip E. Protter
250			_a2nd ed.
260			_bSpringer _c2010 _aGermany
300			_axiii, 419p.
440			_aStochastic modelling and applied probability formally : applications of mathematics
490			_a/ edited by B. Rozovskii; no.21
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 Emery’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.htm
650			_aStochastic integrals
650			_aMartingales (Mathematics)
650			_aStochastic differential equations
942			_cBK
999			_c559537 _d559537