Advertisement

Note on continuous additive functional of the 1-dimensional Brownian path

  • Hiroshi Tanaka
Article

Keywords

Stochastic Process Probability Theory Mathematical Biology Brownian Path 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Blumenthal, R.: An extended Markoff property. Trans. Amer. math. Soc. 85, 52–72 (1957).Google Scholar
  2. [2]
    Dynkin, E. B.: Some transformations of Markov processes. Doklady Akad. Nauk SSSR n. Ser. 133, 269–272 (1960).Google Scholar
  3. [3]
    —: Additive functionals of a Wiener process determined by stochastic integrals. Teor. Verojatn. Primen. 5, 441–452 (1960).Google Scholar
  4. [4]
    Hunt, G. A.: Some theorems concerning Brownian motion. Trans. Amer. math. Soc. 81, 294–319 (1956).Google Scholar
  5. [5]
    ItÔ, K.: On stochastic differential equations. Mem. Amer. math. Soc. No. 4.Google Scholar
  6. [6]
    —: On a formula concerning stochastic differentials. Nagoya math. J. 3, 55–65 (1951).Google Scholar
  7. [7]
    -, and H. P. McKean: Diffusion. (Forthcoming.)Google Scholar
  8. [8]
    Motoo, M.: Diffusion process corresponding to \(\tfrac{1}{2}\sum {\partial ^2 /\partial x^{i^2 } + \sum {b^i (x)\partial /\partial } x^i } \). Ann. Inst. statist. Math. 12, 37–61 (1960).Google Scholar
  9. [9]
    Ventsel, A. D.: Additive functionals of several dimensional Wiener process. Doklady Akad. Nauk SSSR n. Ser. 139, 13–16 (1961).Google Scholar
  10. [10]
    Volkonskii, V. A.: Random substitution of time in strong Markov process. Teor. Verojatn. Primen. 3, 332–350 (1958).Google Scholar

Copyright information

© Springer-Verlag 1963

Authors and Affiliations

  • Hiroshi Tanaka
    • 1
  1. 1.Mathematicae InstituteKyusyu UniversityFukuokaJapan

Personalised recommendations