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MARC 21

Continuous Martingales and Brownian Motion
Tag	Description
020	$a9783662217269$9978-3-662-21726-9
082	$a519.2$223
099	$aOnline resource: Springer
100	$aRevuz, Daniel.
245	$aContinuous Martingales and Brownian Motion$h[EBook] /$cby Daniel Revuz, Marc Yor.
260	$aBerlin, Heidelberg :$bSpringer Berlin Heidelberg :$bImprint: Springer,$c1991.
300	$aIX, 536 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v293
505	$a0. 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.
520	$aThis 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).
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aYor, Marc.$eauthor.
710	$aSpringerLink (Online service)
830	$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v293
856	$uhttp://dx.doi.org/10.1007/978-3-662-21726-9