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Brownian motion : a guide to random processes and stochastic calculus / René L. Schilling ; with a chapter on simulation by Björn Böttcher

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: De Gruyter TextbookPublisher: Berlin : De Gruyter, [2021]Edition: 3rd editionDescription: 1 Online-Ressource (VIII, 500 Seiten) : IllustrationenISBN:
  • 9783110741278
  • 9783110741490
Subject(s): Additional physical formats: 9783110741254 | Erscheint auch als: Brownian motion. Druck-Ausgabe 3rd edition. Berlin : De Gruyter, 2021. XIV, 519 SeitenDDC classification:
  • 519.233
  • 519.2/33 23
  • 510
RVK: RVK: SK 820Local classification: Lokale Notation: math 8LOC classification:
  • QA274.75
DOI: DOI: 10.1515/9783110741278Online resources: Summary: Frontmatter -- Preface -- Contents -- Dependence chart -- 1 Robert Brown’s new thing -- 2 Brownian motion as a Gaussian process -- 3 Constructions of Brownian motion -- 4 The canonical model -- 5 Brownian motion as a martingale -- 6 Brownian motion as a Markov process -- 7 Brownian motion and transition semigroups -- 8 The PDE connection -- 9 The variation of Brownian paths -- 10 Regularity of Brownian paths -- 11 Brownian motion as a random fractal -- 12 The growth of Brownian paths -- 13 Strassen’s functional law of the iterated logarithm -- 14 Skorokhod representation -- 15 Stochastic integrals: L2-Theory -- 16 Stochastic integrals: localization -- 17 Stochastic integrals: martingale drivers -- 18 Itô’s formula -- 19 Applications of Itô’s formula -- 20 Wiener Chaos and iterated Wiener–Itô integrals -- 21 Stochastic differential equations -- 22 Stratonovich’s stochastic calculus -- 23 On diffusions -- 24 Simulation of Brownian motion by Björn Böttcher -- A Appendix -- Bibliography -- IndexSummary: Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''PPN: PPN: 1760896640Package identifier: Produktsigel: EBA-CL-LAEC | EBA-CL-MTPY | EBA-DGALL | EBA-EBKALL | EBA-ECL-LAEC | EBA-ECL-MTPY | EBA-EEBKALL | EBA-ESSHALL | EBA-ESTMALL | EBA-SSHALL | EBA-STMALL | GBV-deGruyter-alles | ZDB-23-DGG | ZDB-23-DMA
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