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＜電子ブック＞
Continuous Martingales and Brownian Motion / by Daniel Revuz, Marc Yor
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 293)

版	1st ed. 1991.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	IX, 536 p : online resource
著者標目	*Revuz, Daniel author Yor, Marc author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical physics FREE:Probability Theory FREE:Theoretical, Mathematical and Computational Physics
一般注記	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 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) HTTP:URL=https://doi.org/10.1007/978-3-662-21726-9

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