• Bert Fristedt
  • Lawrence Gray
Part of the Probability and its Applications book series (PA)


We will treat what many would regard as the most important type of random sequence, for it is both intrinsically natural and also a tool for treating other topics in probability. Martingales are particularly important in the study of Markov sequences and Markov processes, as will be seen later in this book.


Random Walk Random Sequence Stationary Strategy Roulette Wheel Simple Random Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Billingsley, Patrick, Convergence of Probability Measures, John Wiley & Sons, New York, 1968.MATHGoogle Scholar
  2. Dellacherie, Claude and Meyer, Paul-André, Probabilities and Potential B (translated from French, orig. 1980), North-Holland, Amsterdam, 1982.MATHGoogle Scholar
  3. Durrett, Richard, Brownian Motion and Martingales in Analysis, Wadsworth Advanced Books & Software, Belmont, California, 1984.Google Scholar
  4. Durrett, Richard, Stochastic Calculus: A Practical Introduction, CRC Press, Boca Raton, Florida, 1996.MATHGoogle Scholar
  5. Einstein, Albert, Investigations on the Theory of the Brownian Movement, Dover, New York, 1956.MATHGoogle Scholar
  6. Freedman, David, Brownian Motion and Diffusion, Holden-Day, San Francisco, 1971.MATHGoogle Scholar
  7. Friedman, Avner, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York, 1975.MATHGoogle Scholar
  8. Friedman, Avner, Stochastic Differential Equations and Applications, Vol. 2., Academic Press, New York, 1976.MATHGoogle Scholar
  9. Gard, Thomas C, Introduction to Stochastic Differential Equations, Marcel Dekker, New York, 1988.MATHGoogle Scholar
  10. Gihman, I. I. and Skorohod, A. V., Controlled Stochastic Processes, Springer-Verlag, New York, 1979.CrossRefGoogle Scholar
  11. He, Shengwu and Wang, Jiagang and Yan, Jiaan, Semimartingale Theory and Stochastic Calculus, CRC Press, Boca Raton, Florida, 1992.MATHGoogle Scholar
  12. Hida, Takeyuki, Brownian Motion, Springer-Verlag, New York, 1980.MATHGoogle Scholar
  13. Ikeda, Nobuyuki and Watanabe, Shinzo, Stochastic Differential Equations and Diffusion Processes, Second Edition, Kodansha, Tokyo, 1989.MATHGoogle Scholar
  14. Itô, Kiyosi, Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces, Society for Industrial and Applied Mathematics, Philadelphia, 1984.CrossRefGoogle Scholar
  15. Itô, K. and McKean Jr., H. P., Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin, 1974.MATHGoogle Scholar
  16. Krylov, N. V., Introduction to the Theory of Diffusion Processes, American Mathematical Society, Providence, Rhode Island, 1995.Google Scholar
  17. Ledoux, Michel and Talagrand, Michel, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991.CrossRefMATHGoogle Scholar
  18. Lukacs, Eugene, Stochastic Convergence, Second Edition, Academic Press, New York, 1975.MATHGoogle Scholar
  19. McKean Jr., H. P., Stochastic Integrals, Academic Press, New York, 1969.MATHGoogle Scholar
  20. Metivier, Michel and Pellaumail, J., Stochastic Integration, Academic Press, New York, 1980.MATHGoogle Scholar
  21. Metivier, Michel, Semimartingales, a Course on Stochastic Processes, Walter de Gruyter, Berlin, 1982.CrossRefMATHGoogle Scholar
  22. Meyer, Paul A., Probability and Potentials, Blaisdell, Waltham, Massachusetts, 1966.Google Scholar
  23. Nualart, David, The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995.CrossRefMATHGoogle Scholar
  24. Parthasarathy, K. R., Probability Measures on Metric Spaces, Academic Press, New York, 1967.MATHGoogle Scholar
  25. Portenko, N. I., Generalized Diffusion Processes (translation from Russian, orig. 1982), American Mathematical Society, Providence, Rhode Island, 1990.MATHGoogle Scholar
  26. Revuz, Daniel and Yor, Marc, Continuous Martingales and Brownian Motion, Second Edition, Springer-Verlag, Berlin, 1994.MATHGoogle Scholar
  27. Rogers, L. C. G. and Williams, David, Diffusions, Markov Processes, and Martingales, Vol 2: Ito Calculus, John Wiley & Sons, Chichester, 1987.Google Scholar
  28. Skorohod, A. V., Asymptotic Methods in the Theory of Stochastic Differential Equations (translated from Russian, orig. 1987), American Mathematical Society, Providence, Rhode Island, 1989.Google Scholar
  29. Stroock, D. W. and Varadhan, S.R. S., Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979.MATHGoogle Scholar
  30. Yeh, J., Stochastic Processes and the Wiener Integral, Marcel Dekker, New York, 1973.MATHGoogle Scholar
  31. Yor, Marc, Some Aspects of Brownian Motion: Part I: Some Special Functionals, Birkhäuser Verlag, Basel, Switzerland, 1992.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Bert Fristedt
    • 1
  • Lawrence Gray
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations