Handbook of Brownian Motion - Facts and Formulae
The purpose of this book is to give an easy reference to a large number of facts and formulae associated with Brownian motion. The book consists of two parts. The first one - theory part - is devoted to properties of linear diffusions in general and Brown
- PDF / 887,916 Bytes
- 15 Pages / 439.37 x 666.142 pts Page_size
- 62 Downloads / 345 Views
Andrei N. Borodin Paavo Salminen
Handbook of Brownian Motion Facts and Formulae Second Edition
Springer Basel AG
Authors' addresses: Andrei N. Borodin
Paavo Salminen
Steklov Mathematical Institute St. Petersburg Division Fontanka 27 191011 St. Petersburg
Äbo Akademi University Mathematical Institute Fänriksgatan 3 20500 Turku Finland
Russia
2000 Mathematics Subject Classification 60J65, 60J60, 60H05, 60H10, 60J55
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data Borodin, Andrej N.: Handbook of Brownian motion : facts and formulae / Andrei N. Borodin ; Paavo Salminen. - 2. ed. - Basel; Boston ; Berlin : Birkhäuser, 2002 (Probability and its applications) ISBN 978-3-0348-9462-3 ISBN 978-3-0348-8163-0 (eBook) DOI 10.1007/978-3-0348-8163-0
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2002 Springer Basel AG Originally published by Birkhäuser Verlag in 2002 Softcover reprint of the hardcover 2nd edition 2002 Member of the BertelsmannSpringer Publishing Group Printed on acid-free paper produced from chlorine-free pulp. T C F oo ISBN 978-3-0348-9462-3 987654321
www.birkhauser-science.com
CONTENTS
Preface to the first edition
ix
Preface to the second edition
xi xiii
Notation Part I: THEORY
Chapter I.
Stochastic processes in general
1. Basic definitions 2. Markov processes, transition functions, resolvents, and generators 3. Feller processes, Feller-Dynkin processes, and the strong Markov property 4. Martingales
5 7
Basic facts Local time Passage times Additive functionals and killing Excessive functions Ergodic results
12 21 25
Stochastic calculus
Stochastic integration with respect to Brownian motion The Ito and Tanaka formulae Stochastic differential equations - strong solutions Stochastic differential equations - weak solutions One-dimensional stochastic differential equations The Cameron-Martin-Girsanov transformation of measure
Chapter IV. 1. 2. 3. 4. 5. 6. 7.
3
12
Chapter III. 1. 2. 3. 4. 5. 6.
1
Linear diffusions
Chapter II. 1. 2. 3. 4. 5. 6.
1
Brownian motion
Definition and basic properties Brownian local time Excursions Brownian bridge Brownian motion with drift Bessel processes Geometric Brownian motion
27
32 35
38 38 42 44 46 47 48
51
51 54 57 64 67 71 76
CONTENTS
vi
Chapter V. 1. 2. 3. 4. 5.
Local time as a Markov process
Diffusion local time Local time of Brownian motion Local time of Brownian motion with drift Local time of Bessel process Summarizing tables
Chapter VI. Differential systems associated to Brownian motion 1. The Feynman-Kac formula
2. 3. 4. 5.
Exponential stopping Stopping at first exit time Stopping at inverse additive functional Stopping at
Data Loading...
