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OverviewThis book is organized into nine chapters, the first six of which are on 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. The three remaining chapters discuss principle value diffusion times, probabilistic representations of the Riemann zeta function, and progress made on some topics covered in part one. Most of the contents of this text are the subjects of active research, centred on real-value martingales and Brownian mothion, and this volume may be of interest to researchers in probability theory or in more applied fields, such as mathematical finance. Full Product DetailsAuthor: Marc YorPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 1997 ed. Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 0.530kg ISBN: 9783764357177ISBN 10: 3764357177 Pages: 148 Publication Date: 20 March 1997 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents10 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 $$ \left( {\mathcal{F}_t^ - = \varepsilon _t^0;t \geqslant 0} \right)$$ martingales.- 16.2 Some Markov Processes with respect to (? ?a; a ? 0).- 16.3 Some results on $$ \left( {\varepsilon _\infty ^a;a \in \mathbb{R}} \right)$$ 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.ReviewsThis 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. <p>--The Journal of the Indian Inst. of Science <p> 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 """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" 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 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 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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