By Philip E. Protter
It has been 15 years because the first version of Stochastic Integration and Differential Equations, A New Approach seemed, and in these years many different texts at the comparable topic were released, frequently with connections to purposes, particularly mathematical finance. but even with the obvious simplicity of method, none of those books has used the practical analytic approach to offering semimartingales and stochastic integration. hence a second version turns out worthy and well timed, notwithstanding it truly is not acceptable to name it "a new approach".
The new edition has numerous major alterations, so much prominently the addition of workouts 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 workouts were demonstrated by way of graduate scholars at Purdue and Cornell Universities. bankruptcy three has been thoroughly redone, with a brand new, extra intuitive and concurrently trouble-free facts of the basic Doob-Meyer decomposition theorem, the extra common model of the Girsanov theorem because of Lenglart, the Kazamaki-Novikov standards for exponential neighborhood martingales to be martingales, and a contemporary remedy of compensators. bankruptcy four treats sigma martingales (important in finance thought) and provides a extra finished remedy of martingale illustration, together with either the Jacod-Yor idea and Emery’s examples of martingales that truly have martingale illustration (thus going past the traditional instances of Brownian movement and the compensated Poisson process). New issues further comprise an creation to the idea of the growth of filtrations, a therapy of the Fefferman martingale inequality, and that the twin area of the martingale area H^1 might be pointed out with BMO martingales. options to chose workouts can be found on the site of the writer, with present URL http://www.orie.cornell.edu/~protter/books.html.
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