Download for FREE in 4 easy steps...
This is a Premium eBook - get it free for 30 days
You can also read this in Bookboon.com Premium
In this book the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process...
300+ Business books exclusively in our Premium eReader
- No adverts
- Advanced features
- Personal library
Users who viewed this item also viewed
Advanced stochastic processes: Part II
Stochastic Processes 2 - Probability Examples c-9
Stochastic Processes 1 - Probability Examples c-8
Stochastic Processes for Finance
Random variables II - Probability Examples c-3
Random variables III - Probability Examples c-4
Continuous Distributions - Probability Examples c-6
Introduction to Probability - Probability Examples c-1
About the book
In this book, which is basically self-contained, the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process, and Brownian motion as a martingale. Brownian motion can also be considered as a functional limit of symmetric random walks, which is, to some extent, also discussed. Related topics which are treated include Markov chains, renewal theory, the martingale problem, Itô calculus, cylindrical measures, and ergodic theory. Convergence of measures, stochastic differential equations, Feynman-Kac semigroups, and the Doob-Meyer decomposition theorem theorem are discussed in the second part of the book.
Chapter 1. Stochastic processes: prerequisites
1. Conditional expectation
2. Lemma of Borel-Cantelli
3. Stochastic processes and projective systems of measures
4. A definition of Brownian motion
5. Martingales and related processes
Chapter 2. Renewal theory and Markov chains
1. Renewal theory
2. Some additional comments on Markov processes
3. More on Brownian motion
4. Gaussian vectors
5. Radon-Nikodym Theorem
6. Some martingales
Chapter 3. An introduction to stochastic processes: Brownian motion...
1. Gaussian processes
2. Brownian motion and related processes
3. Some results on Markov processes, on Feller semigroups and on the martingale problem
4. Martingales, submartingales, supermartingales and semimartingales
5. Regularity properties of stochastic processes
6. Stochastic integrals, Itˆo’s formula
7. Black-Scholes model
8. A version of Fernique’s theorem
About the Author
Since 2009 the author is retired from the University of Antwerp. Until the present day his teaching duties include a course on "Partial Differential Equations and Operators" and one on "Advanced Stochastic Processes". In the sixties the author was a student at the Catholic University of Nijmegen, Netherlands (nowadays Radboud University), and he earned his Ph.D. from the University of Hawaii, USA, (1971). Since 1972 he has been a member of the academic staff of the University of Antwerp, Department of Mathematics and Computer Science, Belgium. Most of his professional life he has been teaching courses in analysis and stochastic processes. His research lies in the area of stochastic analysis. A recent book authored by him is Markov Processes, Feller Semigroups and Evolution Equations, published by WSPC, Singapore, 2011, of about 800 pages.
The embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the bookboon.com website.
The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook
If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on email@example.com and seek permission.