Description
Book SynopsisThis comprehensive guide to stochastic processes covers a wide range of topics. Short, readable chapters aim for clarity rather than full generality and hundreds of exercises are included. Pitched at a level accessible to beginning graduate students, it is both a course book and a rich resource for individual readers.
Trade Review'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
Table of ContentsPreface; 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.
