Brownian Motion

  • O. Hijab
Part of the Applications of Mathematics book series (SMAP, volume 20)


Until now our control systems have been defined over the complex numbers so as to simplify the linear algebra. Since we have no more need to do so, and since Brownian motion is more familiar over the real numbers, from now on we work exclusively in the real domain: henceforth all vectors and matrices will have real values.


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Notes and References

  1. [3.1]
    R. B. Ash, Real Analysis and Probability, Academic Press, New York, 1972.Google Scholar
  2. [3.2]
    J. L. Doob, Stochastic Processes, Wiley, New York, 1952.Google Scholar
  3. [3.3]
    N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.zbMATHGoogle Scholar
  4. [3.4]
    K. Ito, “Stochastic Integral,” Proc. Imperial Acad. Tokyo, 20 (1944), 519–524.zbMATHCrossRefGoogle Scholar
  5. [3.5]
    R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes, Vol. I and II, Springer-Verlag, New York, 1977.zbMATHCrossRefGoogle Scholar
  6. [3.6]
    H. P. McKean, Stochastic Integrals, Academic Press, New York, 1969.zbMATHGoogle Scholar
  7. [3.7]
    E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, NJ, 1967.zbMATHGoogle Scholar
  8. [3.8]
    D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, New York, 1979.zbMATHGoogle Scholar
  9. [3.9]
    S. R. S. Varadhan, Diffusion Problems and Partial Differential Equations, Tata Lecture Notes, Bombay, 1980.zbMATHGoogle Scholar
  10. [3.10]
    N. Wiener, “Differential Space,” J. Math. Phys., 2 (1923), 131–174.Google Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • O. Hijab
    • 1
  1. 1.Mathematics DepartmentTemple UniversityPhiladelphiaUSA

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