Some Aspects of Brownian Motion: Part II: Some Recent Martingale Problems

ISBN-13: 9783764357177 / Angielski / Miękka / 1997 / 148 str.

Marc Yor

Opis

Focuses on topics including expansion of filtration formulae; Burkholder-Gundy inequalities up to any random time; martingales which vanish on the zero set of Brownian motion; the Azema-Emery martingales and chaos representation; the filtration of truncated Brownian motion; and, attempts to characterize the Brownian filtration.

Recenzje

"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

Spis treści

10 On principal values of Brownian and Bessel local times.- 10.1 Yamada’s formulae.- 10.2 A construction of stable processes.- 10.3 Distributions of principal values of Brownian local times, taken at an independent exponential time.- 10.4 Bertoin’s excursion theory for BES( d), 0 < d enjoys the chaos representation property.- 15.3 Some partial results about Azéma’s second martingale.- 15.4 On Emery’s martingales.- Comments on Chapter 15.- 16 The filtration of truncated Brownian motion.- 16.1 The structure of $$ \left( {\mathcal_t^ - = \varepsilon _t^0;t \geqslant 0} \right)$$ martingales.- 16.2 Some Markov Processes with respect to (? ?a; a ? 0).- 16.3 Some results on $$ \left( {\varepsilon _\infty ^a;a \in \mathbb} \right)$$ martingales.- Comments on Chapter 16.- 17 The Brownian filtration, Tsirel’son’s examples, and Walsh’s Brownian motions.- 17.1 On probability measures locally equivalent to Wiener measure.- 17.2 Walsh’s Brownian motions and spider-martingales.- 17.3 Some examples of loss of information for Brownian motion.- Comments on Chapter 17.- Epilogue to Chapter 17.- 18 Complements relative to Part I (Chapters 1 to 9).- 18.0 Some misprints.- 18.1 On Chapter 1.- 18.2 On Chapter 2.- 18.3 On Chapter 3.- 18.4 On Chapter 6.- 18.5 On Chapters 8 and 9.- 18.6 Brownian motion and hyperbolic functions.