By Philip E. Protter
It has been 15 years because the first variation of Stochastic Integration and Differential Equations, A New Approach seemed, and in these years many different texts at the similar topic were released, frequently with connections to purposes, particularly mathematical finance. but even with the plain simplicity of process, none of those books has used the useful analytic approach to featuring semimartingales and stochastic integration. hence a second variation turns out worthy and well timed, although it truly is not acceptable to name it "a new approach".
The new edition has a number of major adjustments, so much prominently the addition of routines for resolution. those are meant to complement the textual content, yet lemmas wanted in an explanation are by no means relegated to the workouts. some of the routines were verified through graduate scholars at Purdue and Cornell Universities. bankruptcy three has been thoroughly redone, with a brand new, extra intuitive and at the same time simple facts of the elemental Doob-Meyer decomposition theorem, the extra common model of the Girsanov theorem as a result of Lenglart, the Kazamaki-Novikov standards for exponential neighborhood martingales to be martingales, and a contemporary therapy of compensators. bankruptcy four treats sigma martingales (important in finance conception) and offers a extra accomplished remedy of martingale illustration, together with either the Jacod-Yor conception and Emery’s examples of martingales that really have martingale illustration (thus going past the normal circumstances of Brownian movement and the compensated Poisson process). New issues additional comprise an creation to the speculation of the growth of filtrations, a remedy of the Fefferman martingale inequality, and that the twin house of the martingale area H^1 could be pointed out with BMO martingales. options to chose routines can be found on the website of the writer, with present URL http://www.orie.cornell.edu/~protter/books.html.