Advanced stochastic processes: Part I Jan A Van Casteren Download free books at Jan A Van Casteren Advanced Stochastic Processes Part I ii Download free eBooks at bookboon.com Advanced stochastic processes: Part I 2nd edition © 2015 Jan A Van Casteren & bookboon.com ISBN 978-87-403-1115-0 he author is obliged to Department of Mathematics and Computer Science of the University of Antwerp for its material support he author is also indebted to Freddy Delbaen (ETH, Zürich), and the late Jean Haezendock (University of Antwerp) A big part of Chapter is due to these people he author is thankful for comments and logistic support by numerous students who have taken courses based on this text In particular, he is grateful to Lieven Smits and Johan Van Biesen (former students at the University of Antwerp) who wrote part of the Chapters and he author gratefully acknowledges World Scientic Publishers (Singapore) for their permission to publish the contents of Chapter which also makes up a substantial portion of Chapter in [144] he author also learned a lot from the book by Stirzaker [124] Section of Chapter is taken from [124], and the author is indebted to David Stirzaker to allow him to include this material in this book he author is also grateful to the people of Bookboon, among whom Karin Hamilton Jakobsen and Ahmed Zsolt Dakroub, who assisted him in the inal stages of the preparation of this book iii Download free eBooks at bookboon.com Advanced stochastic processes: Part I Contents Contents Preface i Chapter Stochastic processes: prerequisites Conditional expectation Lemma of Borel-Cantelli Stochastic processes and projective systems of measures A definition of Brownian motion Martingales and related processes 10 16 17 Chapter Renewal theory and Markov chains Renewal theory Some additional comments on Markov processes More on Brownian motion Gaussian vectors Radon-Nikodym Theorem Some martingales 35 35 61 70 76 78 78 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative technologies and new markets provide both opportunities and challenges An environment in which your expertise is in high demand Enjoy the supportive working atmosphere within our global group and beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every day Light is OSRAM Download free eBooks at bookboon.com Click on the ad to read more Advanced stochastic processes: Part I Contents Chapter An introduction to stochastic processes: Brownian motion, Gaussian processes and martingales Gaussian processes Brownian motion and related processes Some results on Markov processes, on Feller semigroups and on the martingale problem Martingales, submartingales, supermartingales and semimartingales Regularity properties of stochastic processes Stochastic integrals, Itˆo’s formula Black-Scholes model An Ornstein-Uhlenbeck process in higher dimensions A version of Fernique’s theorem 10 Miscellaneous 89 89 98 117 147 151 162 188 197 221 223 360° thinking Discover the truth at www.deloitte.ca/careers Download free eBooks at bookboon.com © Deloitte & Touche LLP and affiliated entities Click on the ad to read more ... Radon-Nikodym Theorem Some martingales 35 35 61 70 76 78 78 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite spectrum of possibilities: Innovative... and beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every... Van Casteren Advanced Stochastic Processes Part I ii Download free eBooks at bookboon.com Advanced stochastic processes: Part I 2nd edition © 2015 Jan A Van Casteren & bookboon.com ISBN 978-87-403-1115-0