Stochastic Processes

Erscheinungsjahr 2015
ISBN: 978-1-107-00800-7
Verlag: Cambridge University Press

Buch, Englisch, Band 33, 406 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 959 g

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Autoren/Hrsg.

Bass, Richard F.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

Preface; 1. Basic notions; 2. Brownian motion; 3. Martingales; 4. Markov properties of Brownian motion; 5. The Poisson process; 6. Construction of Brownian motion; 7. Path properties of Brownian motion; 8. The continuity of paths; 9. Continuous semimartingales; 10. Stochastic integrals; 11. Itô's formula; 12. Some applications of Itô's formula; 13. The Girsanov theorem; 14. Local times; 15. Skorokhod embedding; 16. The general theory of processes; 17. Processes with jumps; 18. Poisson point processes; 19. Framework for Markov processes; 20. Markov properties; 21. Applications of the Markov properties; 22. Transformations of Markov processes; 23. Optimal stopping; 24. Stochastic differential equations; 25. Weak solutions of SDEs; 26. The Ray–Knight theorems; 27. Brownian excursions; 28. Financial mathematics; 29. Filtering; 30. Convergence of probability measures; 31. Skorokhod representation; 32. The space C[0, 1]; 33. Gaussian processes; 34. The space D[0, 1]; 35. Applications of weak convergence; 36. Semigroups; 37. Infinitesimal generators; 38. Dirichlet forms; 39. Markov processes and SDEs; 40. Solving partial differential equations; 41. One-dimensional diffusions; 42. Lévy processes; A. Basic probability; B. Some results from analysis; C. Regular conditional probabilities; D. Kolmogorov extension theorem; E. Choquet capacities; Frequently used notation; Index.

Über Autor(innen)

Bass, Richard F.
Richard F. Bass is Board of Trustees Distinguished Professor in the Department of Mathematics at the University of Connecticut.