E-Book, Englisch, 536 Seiten, Web PDF
Revuz / Yor Continuous Martingales and Brownian Motion
Erscheinungsjahr 2013
ISBN: 978-3-662-21726-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 536 Seiten, Web PDF
Reihe: Grundlehren der mathematischen Wissenschaften
ISBN: 978-3-662-21726-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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).
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Weitere Infos & Material
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.
