Brownian Motion

Erscheinungsjahr 2016
ISBN: 978-0-521-76018-8
Verlag: Cambridge University Press

Buch, Englisch, Band 30, 416 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 974 g

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Autoren/Hrsg.

Mörters, Peter

Peres, Yuval

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik Atom- und Molekülphysik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

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.

Über Autor(innen)

Mörters, Peter
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).

Peres, Yuval
Yuval Peres is a Principal Researcher at Microsoft Research in Redmond, WA. He is also an Adjunct Professor at the University of California, Berkeley and at the University of Washington. His research interests include most areas of probability theory, as well as parts of ergodic theory, game theory, and information theory.