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 Electronic Communications in Probability > Vol. 6 (2001) > Paper 9 open journal systems 


Kendall's identity for the first crossing time revisited

Konstantin Borovkov, University of Melbourne
Zaeem Burq, University of Melbourne


Abstract
We give a new relatively compact proof of the famous identity for the distribution of the first hitting time of a linear boundary by a skip-free process with stationary independent increments. The proof uses martingale identities and change of measure.


Full text: PDF

Pages: 91-94

Published on: August 3, 2001


Bibliography
  1. Barton, D. E., and Mallows, C. L. (1965), Some aspects of the random sequence, Ann. Math. Statist. 36, 236-260. Math. Review 31 #2745
  2. Borovkov, A. A. (1965), On the first passage time for a class of processes with independent increments, Theor. Probab. Appl. 10, 360-364. [In Russian.] Math. Review 31 #6276
  3. Borovkov, A. A. (1976), Stochastic processes in queueing theory, Springer, New York. Math. Review 52 #12118
  4. Borovkov, K. A. (1995), On crossing times for multidimensional walks with skip-free components, J. Appl. Prob. 32, 991-1006. Math. Review 97c:60121
  5. Feller, W. (1971), An introduction to probability theory and its applications. Vol. 2. 2nd edn. Wiley, New York. Math. Review 42 #5292
  6. Keilson, J. (1963), The first passage time density for homogeneous skip-free walks on the continuum, Ann. Math. Statist. 34, 1003-1011. Math. Review 27 #3029
  7. Kendall, D. G. (1957), Some problems in theory of dams, J. Royal Stat. Soc. B, 19, 207-212. Math. Review 19,1092g
  8. Rogozin, B. A. (1966), Distribution of certain functionals related to boundary value problems for processes with independent increments, Theor. Probab. Appl. 11, 161-169. [In Russian.] Math. Review 34 #8491
  9. Skorohod, A. V. (1964), Random processes with independent increments, Nauka, Moscow. [In Russian. English translation of the second Russian edition was published in 1991 by Kluwer, Dordrecht.] Math. Review 31 #6280
  10. Takács, L. (1967), Combinatorial methods in the theory of stochastic processes. Wiley, New York. Math. Review 36 #947
  11. Zolotarev, V. M. (1964), The first passage time of a level and the behaviour at infinity of a class of processes with independent increments, Theor. Probab. Appl. 9, 724-733. [In Russian.] Math. Review 30 #1546
















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Electronic Communications in Probability. ISSN: 1083-589X