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Probabilty Theory - Durrett - i Probability Theory and...

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i Probability: Theory and Examples Rick Durrett January 29, 2010 Copyright 2010, All rights reserved.
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ii
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Preface Some times the lights are shining on me. Other times I can barely see. Lately it occurs to me what a long strange trip its been. Grateful Dead In 1989 when the first edition of the book was completed, my sons David and Greg were 3 and 1, and the cover picture showed the Dow Jones at 2650. The last twenty years have brought many changes but the song remains the same. The title of the book indicates that as we develop the theory, we will focus our attention on examples. Hoping that the book would be a useful reference for people who apply probability in their work, we have tried to emphasize the results that are important for applications, and illustrated their use with roughly 200 examples. Probability is not a spectator sport, so the book contains almost 450 exercises to challenge the reader and to deepen their understanding. The fourth edition has two major changes (in addition to a new publisher): (i) The book has been converted from TeX to LaTeX. The systematic use of labels should eventually eliminate problems with references to other points in the text. In addition, the picture enviroment and graphicx package has allowed for the figures lost from the third edition to be reintroduced, and a number of new ones to be added. (ii) Four sections of the old appendix have been combined with the first three section of Chapter 1 to make a new first chapter on measure theory, which should allow the book to be used by people who do not have this background without making the text tedious for those who have. Acknowledgements. I am always grateful to the many people who sent me comments and typos. Helping to correct the first edition were David Aldous, Ken Alexander, Daren Cline, Ted Cox, Robert Dalang, Joe Glover, David Griffeath, Phil Griffin, Joe Horowitz, Olav Kallenberg, Jim Kuelbs, Robin Pemantle, Yuval Peres, Ken Ross, Byron Schmuland, Steve Samuels, Jon Wellner, and Ruth Williams. The third edition benefitted from input from Manel Baucells, Eric Blair, Zhen- Qing Chen, Ted Cox, Bradford Crain, Winston Crandall, Finn Christensen, Amir Dembo, Neil Falkner, Changyong Feng, Brighten Godfrey, Boris Granovsky, Jan Hannig, Andrew Hayen, Martin Hildebrand, Kyoungmun Jang, Anatole Joffe, Daniel Kifer, Steve Krone, Greg Lawler, T.Y. Lee, Shlomo Levental, Torgny Lindvall, Arif Mardin, Carl Mueller, Robin Pemantle, Yuval Peres, Mark Pinsky, Ross Pinsky, Boris Pittel, David Pokorny, Vinayak Prabhu, Brett Presnell, Jim Propp, Yossi Schwarz- fuchs, Rami Shakarchi, Lian Shen, Marc Shivers, Rich Sowers, Bob Strain, Tsachy Weissman, and Hao Zhang. New helpers for the fourth edition include John Angus, Phillipe Charmony, Adam Cruz, Ricky Der, Justin Dyer, Piet Groeneboom, Vlad Island, Elena Kosygina, Richard Laugesen, Sungchul Lee, Shlomo Levental, Ping Li, Fredddy L´ opez, Piotr Milos, iii
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iv Davey Owen, Brett Presnell, Alex Smith, Harsha Wabgaonkar, John Walsh, Tsachy Weissman, Neil Wu, Ofer Zeitouni, Martin Zerner, Andrei Zherebtsov. I apologize to those whose names have been omitted or are new typos.
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