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Upper bounds of the Gärtner-Ellis theorem for the sequences of random variables

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  • Nyrhinen, Harri

Abstract

Let Y1,Y2,... be real valued random variables. The Gärtner-Ellis theorem gives sufficient conditions for a large deviations principle for the sequence {Yn/n}. Briefly, the theorem provides sufficient conditions for exponential upper bounds for the probabilities P(Yn/n[set membership, variant]F) for the closed sets F and lower bounds for the probabilities P(Yn/n[set membership, variant]G) for the open sets G. Our objective is to derive necessary and sufficient conditions for the upper bounds of the theorem.

Suggested Citation

  • Nyrhinen, Harri, 2005. "Upper bounds of the Gärtner-Ellis theorem for the sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 57-60, June.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:1:p:57-60
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    Cited by:

    1. Harri Nyrhinen, 2015. "On real growth and run-off companies in insurance ruin theory," Papers 1511.01763, arXiv.org.

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