### Abstract

Original language | English |
---|---|

Place of Publication | Cambridge |

Publisher | Cambridge University Press |

Volume | 30 |

ISBN (Print) | 9780521760188 |

Publication status | Published - 2010 |

### Publication series

Name | Cambridge Series in Statistical and Probabilistic Mathematics |
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Publisher | Cambridge University Press |

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### Cite this

*Brownian motion*. (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.

**Brownian motion.** / Morters, Peter; Peres, Yuval.

Research output: Book/Report › Book

*Brownian motion*. Cambridge Series in Statistical and Probabilistic Mathematics, vol. 30, Cambridge University Press, Cambridge.

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TY - BOOK

T1 - Brownian motion

AU - Morters, Peter

AU - Peres, Yuval

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

M3 - Book

SN - 9780521760188

VL - 30

T3 - Cambridge Series in Statistical and Probabilistic Mathematics

BT - Brownian motion

PB - Cambridge University Press

CY - Cambridge

ER -