Advertisement

Local times for Markov processes

  • R. M. Blumenthal
  • R. K. Getoor
Article

Keywords

Stochastic Process Probability Theory Markov Process Local Time Mathematical Biology 
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]
    Austin, D. G., R. M. Blumenthal, and R. V. Chacon: On continuity of transition functions. Duke math. J. 25, 533–542 (1958).Google Scholar
  2. [2]
    Blumenthal, R. M., and R. K. Getoor: Sample functions of stochastic processes with stationary independent increments. J. Math. Mech., 10, 493–516 (1961).Google Scholar
  3. [3]
    —, and H. P. McKean, Jr.: Markov processes with identical hitting distributions. Illinois J. Math. 6, 402–420 (1962).Google Scholar
  4. [4]
    - Additive functional of Markov processes in duality. To appear in Trans. Amer. math. Soc.Google Scholar
  5. [5]
    Bochner, S.: Harmonic analysis and the theory of probability. Berkeley and Los Angeles, Univ. of Calif. Press. 1955.Google Scholar
  6. [6]
    Boylan, E.S.: Local times for a class of Markov processes. Illinois J. Math. 8, 19–39 (1964).Google Scholar
  7. [7]
    Dynkin, E. B.: Theory of Markov processes (English translation) Englewood Cliffs, N.J., Prentice-Hall, 1961.Google Scholar
  8. [8]
    Getoor, R. K.: The asymptotic distribution of the number of zero free intervals of a stable process. Trans. Amer. math. Soc., 106, 127–138 (1963).Google Scholar
  9. [9]
    Hunt, G. A.: Markov processes and potentials I, II, and III. Illinois. J. Math., 1, 44–93, 316–369 (1957), and 2, 151–213 (1958).Google Scholar
  10. [10]
    Karlin, S., and J. McGregor: Classical diffusion processes and total positivity. Journ. Math. Anal. and Appl., 1, 163–183 (1960).Google Scholar
  11. [11]
    Lamperti, J.: An invariance principle in renewal theory. Ann. math. Statistics, 33, 685–696 (1962).Google Scholar
  12. [12]
    McKean, H. P., jr., and K. Ito: Diffusion theory, forthcoming book.Google Scholar
  13. [13]
    Meyer, P. A.: Fonctionelles multiplicatives et additives de Markov. Ann. Inst. Fourier, 12, 125–230 (1962).Google Scholar
  14. [14]
    Stone, C. J.: The set of zeros of a semi-stable process. Illinois Journ. Math., 7, 631–637 (1963).Google Scholar
  15. [15]
    šur, M. G.: Continuous additive functionals of a Markov process. Doklady Akad. Nauk. SSSR, n. Ser. 137, 800–803, (1961) (in Russian). Translated in Soviet Mathematics, 2, 365–368 (1961).Google Scholar
  16. [16]
    Trotter, H. F.: A property of Brownian motion paths. Illinois J. Math., 2, 425–433 (1958).Google Scholar
  17. [17]
    Volkonski, V. A.: Additive functionals of a Markov process. Trudy Moskovsk math. Obšč., 9, 143–189 (1960) (in Russian).Google Scholar

Copyright information

© Springer-Verlag 1964

Authors and Affiliations

  • R. M. Blumenthal
    • 1
  • R. K. Getoor
    • 1
  1. 1.University of WashingtonSeattle 5, WashingtonUSA

Personalised recommendations