Stochastic Process Doob Pdf Download REPACK
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This class is an introduction to stochastic integration and stochastic differential equations for continuous semimartingales. Expected background includes the contentsof the Math 280 full course in graduate probability. In particular, students should already be familiar with the basics of stochastic processes (filtrations, stoppingtimes, quadratic variation, Brownian motion and other continuous Markov processes) and martingales (optional stopping, local martingales, Doob-Meyer decomposition). After briefly reviewing these topics, we will develop the stochastic integral with respect to Brownian motion, and then generalize this to predictable processes. We thenproceed to Ito's formula, and the standard theory of existence and uniqueness for stochastic differential equations (SDEs). Time permitting, we will conclude with a briefdiscussion of white noise and stochastic partial differential equations (SPDEs).
Text Resources:The main text resource we will follow for the course are the Lecture Notes produced by Vaki Nikitopoulos from a previous iteration of this course, found here.These notes partially follow the development in the textbook Intorduction to Stochastic Integration (Second Edition) by Chung and Williams; it is available at the UCSD bookstore, and also free to UCSD affiliates as a pdf download from SpringerLink. The recent textbook \"An Introduction through Theory and Exercises\" by Baldi is a good alternate source for this material. It is available for free to UCSD affiliates as a pdf download from SpringerLink. Seppalainen's very polished notes give a more comprehensive treatment than we need: Basics of Stochastic Analysis. For the necessary background in measure theory, probability theory, and stochastic processes, please see my year-long YouTube course. 153554b96e
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