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© 1997

Some Aspects of Brownian Motion

Part II: Some Recent Martingale Problems

Book

Part of the Lectures in Mathematics ETH Zürich book series (LM)

About this book

Introduction

The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993. Part I, the elder brother of the present book [Part II], aimed at the computation, as explicitly as possible, of a number of interesting functionals of Brownian motion. It may be natural that Part II, the younger brother, looks more into the main technique with which Part I was "working", namely: martingales and stochastic calculus. As F. Knight writes, in a review article on Part I, in which research on Brownian motion is compared to gold mining: "In the days of P. Levy, and even as late as the theorems of "Ray and Knight" (1963), it was possible for the practiced eye to pick up valuable reward without the aid of much technology . . . Thereafter, however, the rewards are increasingly achieved by the application of high technology". Although one might argue whether this golden age is really foregone, and discuss the "height" of the technology involved, this quotation is closely related to the main motivations of Part II: this technology, which includes stochastic calculus for general discontinuous semi-martingales, enlargement of filtrations, . . .

Keywords

Brownian motion Markov process Martingale Probability theory filtration function local time

Authors and affiliations

  1. 1.Laboratoire de ProbabilitésUniversité Pierre et Màrie CurieParis Cedex 05France

Bibliographic information

  • Book Title Some Aspects of Brownian Motion
  • Book Subtitle Part II: Some Recent Martingale Problems
  • Authors Marc Yor
  • Series Title Lectures in Mathematics ETH Zürich
  • DOI https://doi.org/10.1007/978-3-0348-8954-4
  • Copyright Information Birkhäuser Verlag 1997
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-7643-5717-7
  • eBook ISBN 978-3-0348-8954-4
  • Edition Number 1
  • Number of Pages XII, 148
  • Number of Illustrations 4 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site

Reviews

"This is a formidable book, and is meant for the specialist...this book (together with Part I) can be very rewarding, imparting a very good insight into the subtelities of martinglae theory and stochastic calculus."   

--The Journal of the Indian Inst. of Science

 

"All efforts are rewarded by acknowledgment with modern point of view on such a popular object as Brownian motion and on still open problems related to it." -Zeitschrift fur Mathematik