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Stochastic Processes


Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: October 2011
  • availability: Available
  • format: Hardback
  • isbn: 9781107008007

£ 65.99

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About the Authors
  • 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.

    • Unlike existing books, is uniquely designed for graduate students
    • Fully equips students to tackle the research literature and includes 350 exercises so readers can put the theory into practice
    • Covers all of the necessary material for a first-year graduate course in probability
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: October 2011
    • format: Hardback
    • isbn: 9781107008007
    • length: 408 pages
    • dimensions: 254 x 183 x 25 mm
    • weight: 0.91kg
    • contains: 2 b/w illus. 350 exercises
    • availability: Available
  • Table of Contents

    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

  • Resources for

    Stochastic Processes

    Richard F. Bass

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  • Instructors have used or reviewed this title for the following courses

    • Business Optimization
    • Stochastic Processes with Applications
  • Author

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

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