Brownian Motion

Informationen zum Autor Peter Mörters is Professor of Probability and ESPRC Advanced Research Fellow at the University of Bath. His research on Brownian motion includes identification of the tail behaviour of intersection local times (with König), the multifractal structure of intersections (with Klenke), and the exact packing gauge of double points of three-dimensional Brownian motion (with Shieh). Klappentext Everything the graduate student in probability wants to know about Brownian motion, including the latest research in the field. Zusammenfassung This eagerly awaited graduate-level textbook covers all the essential elements of the theory of Brownian motion! a core area of probability theory! as well as the most recent research. The authors' focus on sample path properties presents a unique and modern point of view. Inhaltsverzeichnis Preface; Frequently used notation; Motivation; 1. Brownian motion as a random function; 2. Brownian motion as a strong Markov process; 3. Harmonic functions, transience and recurrence; 4. Hausdorff dimension: techniques and applications; 5. Brownian motion and random walk; 6. Brownian local time; 7. Stochastic integrals and applications; 8. Potential theory of Brownian motion; 9. Intersections and self-intersections of Brownian paths; 10. Exceptional sets for Brownian motion; Appendix A. Further developments: 11. Stochastic Loewner evolution and its applications to planar Brownian motion; Appendix B. Background and prerequisites; Hints and solutions for selected exercises; References; Index.

Product details

• Authors: Peter Morters, Peter Peres Morters, Peter Mörters, Yuval Peres
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 25.03.2010
• EAN: 9780521760188
• ISBN: 978-0-521-76018-8
• No. of pages: 416
• Series: Cambridge Series in Statistical and Probabilistic Mathematics; Cambridge Series in Statistical and Probabilistic; Cambridge Series in Statistical and Probabilistic Mathematics; Cambridge Series in Statistical and Probabilistic
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics