Stochastic Processes

Comprehensive guide to stochastic processes. Accessible to beginning graduate students and researchers from applied disciplines.

Richard F. Bass (Author)

9781107008007, Cambridge University Press

Hardback, published 6 October 2011

408 pages, 2 b/w illus. 350 exercises
25.4 x 18.3 x 2.5 cm, 0.91 kg

'The author of this book is well recognized for his long standing and successful work in the area of stochastic processes … this book represents quite well the modern state of the art of the theory of stochastic processes. There are good reasons to strongly recommend the book to graduate and postgraduate students taking an advanced course in stochastic processes.' Jordan M. Stoyanov, Zentralblatt MATH

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.

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.

Subject Areas: Stochastics [PBWL], Probability & statistics [PBT]