Franklin

Brownian motion [electronic resource] : an introduction to stochastic processes / René L. Schilling, Lothar Partzsch ; with a chapter on simulation by Björn Böttcher.

Author/Creator:
Schilling, René L.
Publication:
Berlin ; Boston : De Gruyter, c2012.
Format/Description:
Book
1 online resource (396 p.)
Series:
De Gruyter graduate.
De Gruyter graduate
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Subjects:
Brownian motion processes.
Stochastic processes.
Form/Genre:
Electronic books.
Language:
English
Summary:
Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors' aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.
Contents:
Front matter
Preface
Contents
Dependence chart
Index of notation
Chapter 1. Robert Brown's new thing
Chapter 2. Brownian motion as a Gaussian process
Chapter 3. Constructions of Brownian motion
Chapter 4. The canonical model
Chapter 5. Brownian motion as a martingale
Chapter 6. Brownian motion as a Markov process
Chapter 7. Brownian motion and transition semigroups
Chapter 8. The PDE connection
Chapter 9. The variation of Brownian paths
Chapter 10. Regularity of Brownian paths
Chapter 11. The growth of Brownian paths
Chapter 12. Strassen's Functional Law of the Iterated Logarithm
Chapter 13. Skorokhod representation
Chapter 14. Stochastic integrals: L2-Theory
Chapter 15. Stochastic integrals: beyond L2T
Chapter 16. Itô's formula
Chapter 17. Applications of Itô's formula
Chapter 18. Stochastic differential equations
Chapter 19. On diffusions
Chapter 20. Simulation of Brownian motion / Böttcher, Björn
Appendix
Index
Notes:
Description based upon print version of record.
Includes bibliographical references and index.
Contributor:
Partzsch, Lothar, 1945-
Böttcher, Björn.
ISBN:
1-283-85795-2
3-11-027898-7
OCLC:
796384288
Publisher Number:
10.1515/9783110278989 doi