Brownian Motion : : A Guide to Random Processes and Stochastic Calculus / / René L. Schilling.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2021
• VerfasserIn: Schilling, René L.,
• MitwirkendeR: Böttcher, Björn,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2021]; ©2021
• Year of Publication: 2021
• Edition: 3rd Edition
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XIV, 519 p.)
• Other title: 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 --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110741278; 9783110750720; 9783110750706; 9783110754001; 9783110753776; 9783110754131; 9783110753905
• DOI: 10.1515/9783110741278
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: René L. Schilling.

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''.