Continuous Markov processes and stochastic equations

This is a preview of subscription content, access via your institution.

References

  1. 1.

    S. BernsteinÉquations différentielles stochastiques, Actualités Scientifiques et Industrielles, n. 738, Herman, Paris, 1938, pp. 5–32.

    Google Scholar 

  2. 2.

    M. D. Donsker,An invariance principle for certain probability limit theorems, Memoirs of the American Mathematical Society, Vol. 5 (1951), pp. 43–55.

    MathSciNet  Google Scholar 

  3. 3.

    J. L. Doob,Heuristic approach to the Kolmogorov-Smirnov theorems, Annals of Mathematical Statistics, Vol. 20 (1949), pp. 394–403.

    Article  MathSciNet  Google Scholar 

  4. 4.

    J. L. Doob,Stochastic processes, Wiley, New York, 1953.

    MATH  Google Scholar 

  5. 5.

    P. Erdös and M. Kac,On certain limit theorems of the theory of probability, Bulletin of the American Mathematical Society, Vol. 52 (1946), pp. 292–302.

    Article  MATH  MathSciNet  Google Scholar 

  6. 6.

    W. Feller,Zur Theorie der stochastischen Prozesse, Mathematische Annalen, Vol. 113. (1936), pp. 113–160.

    Article  MathSciNet  Google Scholar 

  7. 7.

    W. Feller,On the integrodifferential equations of purely discontinuous Markoff processes, Transactions of the American Mathematical Society, Vol. 48 (1940), pp. 488–515.

    Article  MathSciNet  MATH  Google Scholar 

  8. 8.

    R. Fortet,Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux derivées partielles du type parabolique, Journal de Mathematiques pures et appliquées, Vol. 22 (1943), pp. 177–243.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    K. Ito,Stochastic integral, Proceedings of the Imperial Academy, Tokyo, Vol. 20 (1944), pp. 519–524.

    MATH  Google Scholar 

  10. 10.

    K. Ito,On a stochastic integral equation, Proceedings of Japan Academy, Vol. 22 (1946) pp. 32–35.

    MATH  Article  Google Scholar 

  11. 11.

    K. Ito,On stochastic differential equations, Memoirs of the American Mathematical Society, Vol. 4 (1951), 51 pp.

  12. 12.

    M. Kac,On some connections between probability theory and differential and integral equations, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1951, pp. 189–215.

    Google Scholar 

  13. 13.

    A. Khintchine,Asymptotische Gesetze der Wahrscheinlichkeitsrechnung, Springer, Berlin, 1933.

    Google Scholar 

  14. 14.

    A. Kolmogoroff,Ueber die analytischen Methoden der Wahrscheinlichkeitsrechnung, Mathematische Annalen, Vol. 104 (1931), pp. 415–458.

    Article  MathSciNet  Google Scholar 

  15. 15.

    G. Maruyama,Markov proceesses and stochastic equations, Natural Science Report, Ochanomizu University, Vol. 4 (1953), pp. 40–43.

    MathSciNet  MATH  Google Scholar 

  16. 16.

    M. Udagawa,Asymptotic properties of distributions of some functionals of random variables, Reports of Statistical Application Research, Union of Japanese Scientists and Engineers, Vol. 2 (1952), pp. 1–66.

    MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Gisiro Maruyama.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Maruyama, G. Continuous Markov processes and stochastic equations. Rend. Circ. Mat. Palermo 4, 48 (1955). https://doi.org/10.1007/BF02846028

Download citation

Keywords

  • Brownian Motion
  • Markov Process
  • Lipschitz Condition
  • Invariance Principle
  • Stochastic Equation