Journal of Mathematical Sciences

, Volume 81, Issue 1, pp 2368–2378 | Cite as

Records in the Fα-scheme. I. Martingale properties

  • P. Deheuvels
  • V. B. Nevzorov
Article
Received:

Abstract

Connections between the records in various models is discussed. Martingale properties for some sequences of random variables connected with the record moments in the Fα-scheme are established. Bibliography: 24 titles.

Keywords

Martingale Property Record Moment 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    R. Ballerini and S. I. Resnick, “Embedding sequences of successive maxima in extremal processes with applications,”J. Appl. Prob.,24, 827–837 (1987).MathSciNetGoogle Scholar
  2. 2.
    K. N. Chandler, “The distribution and frequency of record values,”J. Roy. Statist. Soc.,B 14, 220–228 (1952).MATHMathSciNetGoogle Scholar
  3. 3.
    P. Deheuvels, “On record times associated withkth extremes,” in:Proceedings of the 3rd Pannonian symposium on mathematical statistics, (Visegrad, Hungary, 13–18 Sept., 1982), Akadémiai Kiadó, Budapest (1984), pp. 43–51.Google Scholar
  4. 4.
    P. Deheuvels, “Strong approximations ofkth records andkth record times by Wiener processes,”Probab. Th. Rel. Fields,77, 195–209 (1988).MATHMathSciNetGoogle Scholar
  5. 5.
    W. Dziubdziela and B. Kopocinski, “Limiting properties of thekth record values,”Zastosow. Mat.,15, No. 2, 187–190 (1976).MathSciNetGoogle Scholar
  6. 6.
    H. N. Nagaraya, “Record values and related statistics—a review,”Commun. Statist. Theory Math.,17, 2223–2238 (1988).Google Scholar
  7. 7.
    V. B. Nevzorov, “Two characterizations using records,” in:Lect. Notes Math., Vol. 1233 (1986), pp. 79–85.Google Scholar
  8. 8.
    D. Pfeifer, “Asymptotic expansions for the mean and variance of logarithmic interrecord times,”Methods Oper. Res.,39, 113–121 (1981).MATHGoogle Scholar
  9. 9.
    D. Pfeifer, “A note on moments of certain record statistics,”Z. Wahr. verw. Geb.,66, 293–296 (1984).MathSciNetGoogle Scholar
  10. 10.
    D. Pfeifer, “Extremal processes, secretary problems and the 1/e law,”J. Appl. Probab.,27, 722–733 (1989).MathSciNetGoogle Scholar
  11. 11.
    D. Pfeifer, “Some remarks on the record Nevzorov model,”Adv. Appl. Probab.,23, No. 4, 823–834 (1991).MATHMathSciNetGoogle Scholar
  12. 12.
    A. Renyi, “Theorie des elements saillants d'une suite d'observations,” in:Colloquium in Combinatorial Methods in Probability Theory (1962), pp. 104–117 (see also:Selected Papers of A. Renyi, Vol. 3, Akadémiai Kiadó, Budapest (1976), pp. 50–65).Google Scholar
  13. 13.
    R. W., Shorrock, “On record values and record times,”J. Appl. Probab.,9, No. 2, 316–326 (1972).MATHMathSciNetGoogle Scholar
  14. 14.
    M. C. K. Yang, “On the distribution of the inter-record times in an increasing population,”J. Appl. Probab.,12, 148–154 (1975).MATHGoogle Scholar
  15. 15.
    Ya. Galambos,The Asymptotic Theory of Extremal Order Statistics, Kriger Malabar, Florida (1984).Google Scholar
  16. 16.
    V. B. Nevzorov, “Record times in the case of nonidentically distributed random variables,”Teor. Veroyatn. Primen.,29, No. 4, 808–809 (1984); English transl. inTheory Probab. Appl. Google Scholar
  17. 17.
    V. B. Nevzorov, “On record times and interrecord times for sequences of nonidentically distributed random variables,”Zap. Nauchn. Semin. LOMI,142, 109–118 (1985).MATHMathSciNetGoogle Scholar
  18. 18.
    V. B. Nevzorov, “Onkth-record times and their generalizations,”Zap. Nauchn. Semin. LOMI,153, 115–121 (1986).MATHGoogle Scholar
  19. 19.
    V. B. Nevzorov, “Records,”Teor. Veroyatn. Primen.,32, No. 2, 219–251 (1987).MATHMathSciNetGoogle Scholar
  20. 20.
    V. B. Nevzorov, “Moments of some random variables related with records,”Vestn. Leningr. Univ. Mat. Mekh. Astron., No. 8, 33–37 (1987).MathSciNetGoogle Scholar
  21. 21.
    V. B. Nevzorov, “Distributions ofk-records in the discrete case,”Zap. Nauchn. Semin. LOMI,158, 133–137 (1987).MATHGoogle Scholar
  22. 22.
    V. B. Nevzorov, “Martingale methods of investigation of records,” in:Statistics and Control of Random Processes, Moscow (1989), pp. 133–137.Google Scholar
  23. 23.
    V. B. Nevzorov, “Generating functions fork-record times. Martingale approach,”Zap. Nauchn. Semin. LOMI,184, 208–214 (1990).MATHGoogle Scholar
  24. 24.
    V. B. Nevzorov and A. V. Stepanov, “Records: martingale approach to calculation of moments,” in:Rings and Modules. Limit Theorems of Probability Theory, Issue 2, Leningrad State University, Leningrad (1988), pp. 171–181.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • P. Deheuvels
  • V. B. Nevzorov

There are no affiliations available

Personalised recommendations