On a continuous time extension of Feller's Lemma

  • N. U. Prabhu
  • Michael Rubinovitch


Stochastic Process Probability Theory Mathematical Biology Continuous Time Time Extension 
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  1. 1.
    Baxter, G., Donsker, M.D.: On the distribution of the supremum functional for processes with stationary independent increments. Trans. Amer. math. Soc. 85, 73–87 (1957).Google Scholar
  2. 2.
    Blackwell, D.: Extension of a renewal theorem. Pacific J. Math. 3, 315–320 (1958).Google Scholar
  3. 3.
    Breiman, L.: Probability. Reading: Addison Wesley 1968.Google Scholar
  4. 4.
    Cramér, H.: Collective risk theory. Jubilee Volume of the Skandia Insurance Co., Ab Nordiska Bokhandeln, Stockholm (1955).Google Scholar
  5. 5.
    Feller, W.: On combinatorial methods in fluctuation theory. The Harald Cramer Volume, p. 75–91. New York: John Wiley 1959.Google Scholar
  6. 6.
    —: An introduction to probability theory and its applications, vol. II. New York: John Wiley 1966.Google Scholar
  7. 7.
    Gusak, D.V., Koroljuk, V.S.: On the first passage time across a given level for processes with independent increments. Theor. Probab. Appl. 13, 448–456 (1968).Google Scholar
  8. 8.
    Hunt, G.A.: Some theorems concerning Brownian motion. Trans. Amer. math. Soc. 81, 294–319 (1956).Google Scholar
  9. 9.
    Kemperman, J. H. B.: The first passage problem for a stationary Markov chain. Chicago: University of Chicago Press 1961.Google Scholar
  10. 10.
    Prabhu, N. U.: Ladder variables for a continuous time stochastic process. Z. Wahrscheinlichkeitstheorie verw. Geb. 16, 157–164 (1970).Google Scholar
  11. 11.
    Rubinovitch, M.: Ladder regenerative events with applications to dam models. Ph. D. Thesis, Cornell University 1968.Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • N. U. Prabhu
    • 1
  • Michael Rubinovitch
    • 2
  1. 1.Mathematical Research CenterThe University of WisconsinMadisonUSA
  2. 2.Faculty of Industrial & Management EngineeringTechnionHaifaIsrael

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