Brownian Motion : : A Guide to Random Processes and Stochastic Calculus / / 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...
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| Superior document: | Title is part of eBook package: De Gruyter DG Ebook Package English 2021 |
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2021] ©2021 |
| Year of Publication: | 2021 |
| Edition: | 3rd Edition |
| Language: | English |
| Series: | De Gruyter Textbook
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| Online Access: | |
| Physical Description: | 1 online resource (XIV, 519 p.) |
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Table of Contents:
- 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