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Field name	Details
Dewey Class	519.2
Title	Continuous Martingales and Brownian Motion ([EBook] /) / by Daniel Revuz, Marc Yor.
Author	Revuz, Daniel
Added Personal Name	Yor, Marc author.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1991.
Physical Details	IX, 536 p. : online resource.
Series	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 293
ISBN	9783662217269
Summary Note	This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).:
Contents note	0. Preliminaries -- I. Introduction -- II. Martingales -- III. Markov Processes -- IV. Stochastic Integration -- V. Representation of Martingales -- VI. Local Times -- VII. Generators and Time Reversal -- VIII. Girsanov’s Theorem and First Applications -- IX. Stochastic Differential Equations -- X. Additive Functionals of Brownian Motion -- XI. Bessel Processes and Ray-Knight Theorems -- XII. Excursions -- XIII. Limit Theorems in Distribution -- § 1. Gronwall’s Lemma -- § 2. Distributions -- § 3. Convex Functions -- § 4. Hausdorff Measures and Dimension -- § 5. Ergodic Theory -- Index of Notation -- Index of Terms.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-21726-9
Links to Related Works	Subject References: Mathematics . Physics . Probabilities . Probability theory and stochastic processes . Theoretical, Mathematical and Computational Physics . Authors: Revuz, Daniel . Yor, Marc . Corporate Authors: SpringerLink (Online service) . Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics . Classification: 519.2 .

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Continuous Martingales and Brownian Motion

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