Some Aspects of Brownian Motion

Part II: Some Recent Martingale Problems

Häftad, Engelska, 1997

419 kr

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This 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.

Produktinformation

Utgivningsdatum1997-03-20
Mått155 x 235 x 10 mm
Vikt260 g
FormatHäftad
SpråkEngelska
SerieLectures in Mathematics. ETH Zürich
Antal sidor148
Upplaga1997
FörlagBirkhauser Verlag AG
ISBN9783764357177

Tillhör följande kategorier

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 < denjoys 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.

"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