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

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QA274.2 .B375 2011

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

 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. Ito's formula 12. Some applications of Ito'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. Levy processes A. Basic probability B. Some results from analysis C. Regular conditional probabilities D. Kolmogorov extension theorem E. Choquet capacities Frequently used notation Index.
 (source: Nielsen Book Data)
 Publisher's 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.
(source: Nielsen Book Data)  Supplemental links
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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