Continuous Martingales and Brownian Motion / Grundlehren der mathematischen Wissenschaften Bd.293 (PDF)
(Sprache: Englisch)
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...
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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).
Bibliographische Angaben
- Autoren: Daniel Revuz , Marc Yor
- 2013, 1991, 536 Seiten, Englisch
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3662217260
- ISBN-13: 9783662217269
- Erscheinungsdatum: 29.06.2013
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- Grösse: 39 MB
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Englisch
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