Skip to main content

Prophet inequalities for averages of independent non-negative random variables

Mathematische Zeitschrift volume 192, pages 427–436 (1986)Cite this article

An Erratum to this article was published on 01 January 1996

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (Canada)

References

  1. Chow, Y., Robbins, H., Siegmund, D.: Great expectations: the theory of optimal stopping. Boston, Mass.: Houghton Mifflin, 1971

    Google Scholar 

  2. Cox, D., Kertz, R.: Prophet regions and sharp inequalities forp-th absolute moments of martingales. To appear in J. Multivariate Anal.

  3. Elton, J., Kertz, R.: Comparison of stop rule and maximum expectations for finite sequences of exchangeable random variables, preprint (1985)

  4. Hill, T.: Prophet inequalities and order selection in optimal stopping problems. Proc. Am. Math. Soc.88, 131–137 (1983)

    Google Scholar 

  5. Hill, T., Kertz, R.: Ratio comparisons of supremum and stop rule expectations. Z. Wahrscheinlichkeitstheor. Verw. Geb.56, 283–285 (1981)

    Google Scholar 

  6. Hill, T., Kertz, R.: Additive comparisons of stop rule and supremum expectations of uniformly bounded independent random variables, Proc. Am. Math. Soc.83, 582–585 (1981).

    Google Scholar 

  7. Hill, T., Kertz, R.: Comparisons of stop rule and supremum expectations of i.i.d. random variables. Ann. Probab.10, 336–345 (1982)

    Google Scholar 

  8. Hill, T., Kertz, R.: Stop rule inequalities for uniformly bounded sequences of random variables. Trans. Am. Math. Soc.278, 197–207 (1983)

    Google Scholar 

  9. Kertz, R.: Stop rule and supremum expectations of i.i.d. random variables: a complete comparison by conjugate duality, to appear in J. Multivariate Anal.

  10. Kennedy, D.: Optimal stopping of independent random variables and maximizing prophets. Ann. Probab.13, 566–571 (1985)

    Google Scholar 

  11. Krengel, U., Sucheston, L.: Semiamarts and finite values. Bull. Am. Math. Soc.83, 745–747 (1977)

    Google Scholar 

  12. Krengel, U., Sucheston, L.: On semiamarts, amarts, and processes with finite value. Adv. in Probab. Related Topics4, 197–266 (1978)

    Google Scholar 

  13. Samuel-Cahn, E.: Comparison of threshold stop rules and maximum for independent non-negative random variables. Ann. Probab.12, 1213–1216 (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Theodore P. Hill

Authors
  1. Theodore P. Hill
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by a NATO Postdoctoral Fellowship and NSF Grant DMS-84-01604

An erratum to this article is available at http://dx.doi.org/10.1007/BF02622107.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hill, T.P. Prophet inequalities for averages of independent non-negative random variables. Math Z 192, 427–436 (1986). https://doi.org/10.1007/BF01164017

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01164017