Advanced stochastic processes: Part I Download free books at... Van Casteren Advanced Stochastic Processes Part I Download free eBooks at bookboon.com... Van Casteren & bookboon.com ISB
Trang 1Advanced stochastic processes: Part I
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Trang 2Jan A Van Casteren
Advanced Stochastic Processes
Part I
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Trang 3Advanced 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 5 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 1 and 2 he author gratefully acknowledges World Scientic Publishers (Singapore) for their permission to publish the contents of Chapter 4 which also makes up
a substantial portion of Chapter 1 in [144] he author also learned a lot from the book by Stirzaker [124] Section 1 of Chapter 2 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
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Trang 4Advanced stochastic processes: Part I
4
Contents
Contents
Chapter 1 Stochastic processes: prerequisites 1
3 Stochastic processes and projective systems of measures 10
5 Martingales and related processes 17
Chapter 2 Renewal theory and Markov chains 35
2 Some additional comments on Markov processes 61
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Trang 5Advanced stochastic processes: Part I
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Contents
Chapter 3 An introduction to stochastic processes: Brownian motion,
Gaussian processes and martingales 89
2 Brownian motion and related processes 98
3 Some results on Markov processes, on Feller semigroups and on the
4 Martingales, submartingales, supermartingales and semimartingales 147
5 Regularity properties of stochastic processes 151
6 Stochastic integrals, Itˆo’s formula 162
8 An Ornstein-Uhlenbeck process in higher dimensions 197
9 A version of Fernique’s theorem 221
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