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Dominating points and large deviations for random vectors
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  • Published: December 1996

Dominating points and large deviations for random vectors

  • U. Einmahl1 &
  • J. Kuelbs2 

Probability Theory and Related Fields volume 105, pages 529–543 (1996)Cite this article

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  • 10 Citations

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Summary

We establish a representation formula useful for obtaining precise large deviation probabilities for convex open subsets of a Banach space. These estimates are based on the existence of dominating points in this setting.

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References

  1. Bolthausen, E.: On the probability of large deviations in Banach spaces. Ann. Probab.12, 427–435 (1984)

    Google Scholar 

  2. Csiszar, I.:I-divergence geometry of probability distributions and minimization problems. Ann. Probab.3, 146–158 (1975)

    Google Scholar 

  3. de Acosta, A.: On large deviations of sums of independent random vectors, Probability in Banach Spaces V, Lecture Notes in Mathematics, vol. 1153, pp. 1–14. Berlin: Springer (1985)

    Google Scholar 

  4. de Acosta, A.: Upper bounds for large deviations of dependent random vectors. Z. Wahrsch. verw. Gebiete69, 551–565 (1985)

    Google Scholar 

  5. Dinwoodie, I.H.: Mesures dominantes et Théorème de Sanov. Ann. Inst. Henri Poincaré28, 365–373 (1992)

    Google Scholar 

  6. Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time III. Comm. Pure Appl. Math.29, 389–461 (1976)

    Google Scholar 

  7. Einmahl, U.: Stability results and strong invariance principles for partial sums of Banach space valued random variables. Ann. Probab.17, 333–352 (1989)

    Google Scholar 

  8. Einmahl, U.: Toward a general law of the iterated logarithm in Banach space. Ann. Probab.21, 2012–2045 (1993)

    Google Scholar 

  9. Kuelbs, J., Li, W.V.: Some large deviation results for Gaussian measures. Probability in Banach Spaces IX, Progress in Probab., vol. 35, pp. 251–270. Basel: Birkhäuser (1994)

    Google Scholar 

  10. Ney, P.: Dominating points and asymptotics of large deviations in ℝd. Ann. Probab.11, 158–167 (1983)

    Google Scholar 

  11. Ney, P.: Convexity and large deviations. Ann. Probab.12, 903–906 (1984)

    Google Scholar 

  12. Van Zwet, W.R.: A Berry-Esseen bound for symmetric statistics. Z. Wahrsch. verw. Gebiete66, 425–440 (1984)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    U. Einmahl

  2. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    J. Kuelbs

Authors
  1. U. Einmahl
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  2. J. Kuelbs
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Additional information

Dedicated to Peter Ney on the occasion of his 65th birthday.

Supported in part by NSF Grant DMS-9503665

Supported in part by NSF Grant DMS-9400024

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Cite this article

Einmahl, U., Kuelbs, J. Dominating points and large deviations for random vectors. Probab. Th. Rel. Fields 105, 529–543 (1996). https://doi.org/10.1007/BF01191912

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  • Received: 12 September 1995

  • Revised: 13 December 1995

  • Issue Date: December 1996

  • DOI: https://doi.org/10.1007/BF01191912

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Mathematics Subject Classification (1991)

  • 60B12
  • 60F10
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