UID:
almahu_9947548580402882
Format:
1 online resource (394 p.)
ISBN:
9783110278989
,
9783110288995
Series Statement:
De Gruyter Textbook
Content:
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.
Note:
Frontmatter --
,
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 --
,
Appendix --
,
Index
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012, De Gruyter, 9783110288995
In:
E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012, De Gruyter, 9783110293722
In:
E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012, De Gruyter, 9783110288926
Language:
English
Subjects:
Mathematics
Keywords:
Electronic books
DOI:
10.1515/9783110278989
URL:
https://doi.org/10.1515/9783110278989
URL:
https://doi.org/10.1515/9783110278989
URL:
https://doi.org/10.1515/9783110278989
URL:
Volltext
(lizenzpflichtig)
