- 533 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
About this book
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''.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Brownian Motion by René L. Schilling in PDF and/or ePUB format, as well as other popular books in Mathematics & Business Mathematics. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- 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: L<sup>2</sup>-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