03783nam 22006015 450 991081083790332120211129200646.03-662-06400-610.1007/978-3-662-06400-9(CKB)2660000000027140(SSID)ssj0001296280(PQKBManifestationID)11766117(PQKBTitleCode)TC0001296280(PQKBWorkID)11348123(PQKB)11158428(DE-He213)978-3-662-06400-9(MiAaPQ)EBC3100326(PPN)188265317(EXLCZ)99266000000002714020130107d1999 u| 0engurnn#008mamaatxtccrContinuous Martingales and Brownian Motion /by Daniel Revuz, Marc Yor3rd ed. 1999.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1999.1 online resource (XIII, 602 p.)Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,0072-7830 ;293Bibliographic Level Mode of Issuance: Monograph3-540-64325-7 3-642-08400-1 Includes bibliographical references and indexes.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 -- §6. Probabilities on Function Spaces -- §7. Bessel Functions -- §8. Sturm-Liouville Equation -- Index of Notation -- Index of Terms -- Catalogue.From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..." Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,0072-7830 ;293ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.519.2/8760G44msc60J60mscRevuz Danielauthttp://id.loc.gov/vocabulary/relators/aut54759Yor Marcauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910810837903321Continuous martingales and Brownian motion375923UNINA