Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Stochastic Processes
  • Cited by 58
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2011
Online ISBN:
9780511997044
DOI:
https://doi.org/10.1017/CBO9780511997044
Subjects:
Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, General Statistics and Probability, Statistics and Probability
Series:
Cambridge Series in Statistical and Probabilistic Mathematics (33)
Information

Book description

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.

Reviews

‘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 Source: Zentralblatt MATH

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Page 1 of 2

Contents

Page 1 of 2

References
References
References
Aldous, D. 1978. Stopping times and tightness. Ann. Probab. 6, 335–40.
Barlow, M. T. 1982. One-dimensional stochastic differential equations with no strong solution. J. London Math. Soc. 26, 335–47.
Bass, R. F. 1983. Skorokhod imbedding via stochastic integrals. Séminaire de Probabilités XVII. New York: Springer-Verlag; 221–4.
Bass, R. F. 1995. Probabilistic Techniques in Analysis. New York: Springer-Verlag.
Bass, R. F. 1996. The Doob–Meyer decomposition revisited. Can. Math. Bull. 39, 138–50.
Bass, R. F. 1997. Diffusions and Elliptic Operators. New York: Springer-Verlag.
Billingsley, P. 1968. Convergence of Probability Measures. New York: John Wiley & Sons, Ltd.
Billingsley, P. 1971. Weak Convergence of Measures: Applications in Probability. Philadelphia: SIAM.
Blumenthal, R. M. and Getoor, R. K. 1968. Markov Processes and Potential Theory. New York: Academic Press.
Bogachev, V. I. 1998. Gaussian Measures. Providence, RI: American Mathematical Society.
Boyce, W. E. and DiPrima, R. C. 2009. Elementary Differential Equations and Boundary Value Problems, 9th edn. New York: John Wiley & Sons, Ltd.
Chung, K. L. 2001. A Course in Probability Theory, 3rd edn. San Diego: Academic Press.
Chung, K. L. and Walsh, J. B. 1969. To reverse a Markov process. Acta Math. 123, 225–51.
Dawson, D. A. 1993. Measure-valued Markov processes. Ecole d'Eté de Probabilités de Saint-Flour XXI–1991. Berlin: Springer-Verlag.
Dellacherie, C. and Meyer, P.-A. 1978. Probability and Potential. Amsterdam: North-Holland.
Dudley, R. M. 1973. Sample functions of the Gaussian process. Ann. Probab. 1, 66–103.
Durrett, R. 1996. Probability: Theory and Examples. Belmont, CA: Duxbury Press.
Ethier, S. N. and Kurtz, T. G. 1986. Markov Processes: Characterization and Convergence. New York: John Wiley & Sons, Ltd.
Feller, W. 1971. An Introduction to Probability Theory and its Applications, 2nd edn. New York: John Wiley & Sons, Ltd.
Folland, G. B. 1999. Real Analysis: Modern Techniques and their Applications, 2nd edn. New York: John Wiley & Sons, Ltd.
Fukushima, M., Oshima, Y. and Takeda, M. 1994. Dirichlet Forms and Symmetric Markov Processes. Berlin: de Gruyter.
Gilbarg, D. and Trudinger, N. S. 1983. Elliptic Partial Differential Equations of Second Order, 2nd edn. New York: Springer-Verlag.
Itô, K. and McKean, H. P. Jr 1965. Diffusion Processes and their Sample Paths. Berlin: Springer-Verlag.
Kallianpur, G. 1980. Stochastic Filtering Theory. Berlin: Springer-Verlag.
Karatzas, I. and Shreve, S. E. 1991. Brownian Motion and Stochastic Calculus, 2nd edn. New York: Springer-Verlag.
Knight, F. B. 1981. Essentials of Brownian Motion and Diffusion. Providence, RI: American Mathematical Society.
Kuo, H. H. 1975. Gaussian Measures in Banach Spaces. New York: Springer-Verlag.
Lax, P. 2002. Functional Analysis. New York: John Wiley & Sons, Ltd.
Liggett, T. M. 2010. Continuous Time Markov Processes: An Introduction. Providence, RI: American Mathematical Society.
Meyer, P.-A., Smythe, R. T. and Walsh, J. B. 1972. Birth and death of Markov processes. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. III. Berkeley, CA: University of California Press; 295–305.
Obłój, J. 2004. The Skorokhod embedding problem and its offspring. Probab. Surv. 1, 321–90.
Øksendal, B. 2003. Stochastic Differential Equations: An Introduction with Applications, 6th edn. Berlin: Springer-Verlag.
Perkins, E. A. 2002. Dawson–Watanabe superprocesses and measure-valued diffusions. Lectures on Probability Theory and Statistics (Saint-Flour, 1999). Berlin: Springer-Verlag; 125–324.
Revuz, D. and Yor, M. 1999. Continuous Martingales and Brownian Motion, 3rd edn. Berlin: Springer-Verlag.
Rogers, L. C. G. and Williams, D. 2000a. Diffusions, Markov Processes, and Martingales, Vol. 1. Cambridge: Cambridge University Press.
Rogers, L. C. G. and Williams, D. 2000b. Diffusions, Markov Processes, and Martingales, Vol. 2. Cambridge: Cambridge University Press.
Rudin, W. 1976. Principles of Mathematical Analysis, 3rd edn. New York: McGraw-Hill.
Rudin, W. 1987. Real and Complex Analysis, 3rd edn. New York: McGraw-Hill.
Skorokhod, A. V. 1965. Studies in the Theory of Random Processes. Reading, MA: Addison-Wesley.
Stroock, D. W. 2003. Markov Processes from K. Itô's Perspective. Princeton, NJ: Princeton University Press.
Stroock, D. W. and Varadhan, S. R. S. 1977. Multidimensional Diffusion Processes. Berlin: Springer-Verlag.
Walsh, J. B. 1978. Excursions and local time. Astérisque 52–53, 159–92.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.