Stochastic Processes

  • Michał Kisielewicz
Part of the Springer Optimization and Its Applications book series (SOIA, volume 80)


In this chapter we give a survey of concepts of the theory of stochastic processes. It is assumed that the basic notions of measure and probability theories are known to the reader.


  1. 21.
    Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1976)Google Scholar
  2. 31.
    Friedman, A.: Stochastic Differential Equations and Applications. Academic, New York (1975)zbMATHGoogle Scholar
  3. 33.
    Gihman, I.I., Skorohod, A.V.: The Theory of Stochastic Processes I–III. Springer, Berlin (1974, 1975, 1979)Google Scholar
  4. 43.
    Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North Holland Publ., Amsterdam (1981)zbMATHGoogle Scholar
  5. 44.
    Jacod, J., Shiryaev, A.N.: Limit Theorems for Stochastic Processes. Springer, New York (1987)zbMATHCrossRefGoogle Scholar
  6. 47.
    Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Springer, New York (1991)zbMATHGoogle Scholar
  7. 60.
    Kisielewicz, M.: Stochastic differential inclusions and diffusion processes. J. Math. Anal. Appl. 334, 1039–1054 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 61.
    Kisielewicz, M.: Stochastic representation of partial differential inclusions. J. Math. Anal. Appl. 353, 592–606 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 68.
    Kunita, H.: Stochastic Flows and Stochastic Differential Equations. Cambridge University Press, New York (1990)zbMATHGoogle Scholar
  10. 72.
    Lipcer, R.S., Shiryaev, A.N.: Statistics of Stochastic Processes. PWN, Warszawa (1981) (in Polish)Google Scholar
  11. 86.
    Øksendal, B.: Stochastic Differential Equations. Springer, Berlin (1998)CrossRefGoogle Scholar
  12. 89.
    Protter, P.: Stochastic Integration and Differential Equations. Springer, Berlin (1990)zbMATHCrossRefGoogle Scholar
  13. 94.
    Strook, D.W., Varadhan, S.R.S.: Diffusion processes with continuous coefficients. I, II. Comm. Pure Appl. Math. 22(345–400), 479–530 (1969)Google Scholar
  14. 95.
    Strook, D.W., Varadhan, S.R.S.: Multidimensional Diffusion Processes. Springer, Berlin (1997)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Michał Kisielewicz
    • 1
  1. 1.Faculty of MathematicsUniversity of Zielona GóraZielona GóraPoland

Personalised recommendations