Stochastic processes
 Author/Creator
 Bass, Richard F.
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2011.
 Physical description
 xv, 390 p. : ill. ; 26 cm.
 Series
 Cambridge series on statistical and probabilistic mathematics ; 33.
Access
Available online
 dx.doi.org Cambridge Books Online Access limited to one user.
 proquest.safaribooksonline.com Safari Books Online

Stacks

Unknown
QA274.2 .B375 2011

Unknown
QA274.2 .B375 2011
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 385386) and index.
 Contents

 Machine generated contents note: 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 RayKnight 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. Onedimensional diffusions; 42. Le; vy processes; A. Basic probability; B. Some results from analysis; C. Regular conditional probabilities; D. Kolmogorov extension theorem; E. Choquet capacities; Frequently used notation; Index.
 Summary
 "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 BlackScholes formula for the pricing of derivatives in financial mathematics, the KalmanBucy 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 newfound knowledge to the test and to prepare them for tackling the research literature" Provided by publisher.
 "In a first course on probability one typically works with a sequence of random variables X1, X2, ... For stochastic processes, instead of indexing the random variables by the nonnegative integers, we index them by t G [0, oo) and we think of Xt as being the value at time t. The random variable could be the location of a particle on the real line, the strength of a signal, the price of a stock, and many other possibilities as well. We will also work with increasing families of s fields {Jt}, known as filtrations. The s field Jt is supposed to represent what we know up to time t. 1.1 Processes and s fields Let (Q., J, P) be a probability space. A realvalued stochastic process (or simply a process) is a map X from [0, oo) x Q. to the reals. We write Xt = Xt(?) = X(t, ?). We will impose stronger measurability conditions shortly, but for now we require that the random variables Xt be measurable with respect to J for each t 0. A collection of s fields Jt such that Jt C J for each t and Js C Jt if s t is called a filtration. Define Jt+ = P\e0Jt+e. A filtration is right continuous if Jt+ = Jt for all t 0. " Provided by publisher.
 Supplemental links
 Cover image
Subjects
 Subject
 Stochastic analysis.
Bibliographic information
 Publication date
 2011
 Responsibility
 Richard F. Bass.
 Series
 Cambridge series in statistical and probabilistic mathematics ; 33
 ISBN
 9781107008007
 110700800X