| Description |
1 online resource (ix, 533 pages) : illustrations |
| Series |
Grundlehren der mathematischen Wissenschaften ; 293 |
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Grundlehren der mathematischen Wissenschaften ; 293.
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| Contents |
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 |
| Summary |
This work provides a detailed study of Brownian Motion, via the Itô stochastic calculus of continuous processes, e.g. diffusions, continuous semi-martingales: it should facilitate the reading and understanding of research papers in this area, and be of interest both to graduate students and to more advanced readers, either working primarily with stochastic processes, or doing research in an area involving stochastic processes, e.g. mathematical physics, economics. The emphasis is on methods, rather than generality. After a first introductory chapter, each of the subsequent ones introduces a new method or idea, e.g. stochastic integration, local times, excursions, weak convergence, and describes its appications to Brownian motion; some of these appear for the first time in book form. One of the important features of the book is the large number of exercises which, at the same time, give additional results and will help the reader master the subject more easily |
| Bibliography |
Includes bibliographical references (pages 505-526) and indexes |
| Notes |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
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digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
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Print version record |
| Subject |
Martingales (Mathematics)
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Brownian motion processes.
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Brownian motion processes.
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Martingales (Mathematics)
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Brownsche Bewegung
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Martingal
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Stochastische Analysis
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Martingaltheorie
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Stochastische processen.
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Martingales (Mathématiques)
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Mouvement brownien.
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| Form |
Electronic book
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| Author |
Yor, Marc
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| ISBN |
9783662217269 |
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3662217260 |
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9783662217283 |
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3662217287 |
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