Skip to main content
Log in

Asymptotic discrimination between renewal processes

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Limit theorems for the logarithm of the likelihood ratio are proven. With their help the rate of decrease in the probability of errors of the second kind in the Neumann-Pierson criterion is established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. Yu. N. Linkov and Munir al Shakhf, Asymptotic Properties of the Likelihood Ratio for Counting Processes [Russian Preprint], Akad. Nauk SSSR, Inst. Prikl. Mat. Mekh., Donetsk (1991), p. 56.

    Google Scholar 

  2. D. Cox and P. Lewis, Statistical Analysis of Time Series [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  3. D. Cox and M. Smith, Renewal Theory [Russian translation], Sov. Radio, Moscow (1967), p. 300.

    Google Scholar 

  4. Yu. M. Kabanov, P. Sh. Lintser, and A. N. Shiryaev, “Martingale techniques in the theory of point processes,” in: Trans. Workshop on the Theory of Random Processes (Druskininkai, Nov. 25–28, 1974), Vilnius (1975), Ch. 2, pp. 269–354.

  5. J. Jacod, “Multivariate point processes: predictable projection, Radon-Nikoym derivatives, representation of Martingales,” Z. Warscheinlichkeitstheor. und Verw Geb.,31, No. 3, 235–253 (1975).

    Google Scholar 

  6. W. Feller, “Fluctuation theory of recurrent events,” Trans. Amer. Math. Soc.,67, No. 1, 98–119 (1949).

    Google Scholar 

  7. Yu. N. Linkov, Asymptotic discrimination between two simple statistical hypotheses [Russian Preprint], Akad. Nauk SSSR, Inst. Matematiki, 86.45, Kiev (1986), p. 60.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1382–1388, October, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin'kov, Y.N., Shakhf, M.a. Asymptotic discrimination between renewal processes. Ukr Math J 44, 1268–1275 (1992). https://doi.org/10.1007/BF01057684

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01057684

Keywords

Navigation