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

Harri Nyrhinen

Statistics & Probability Letters, 2005, vol. 73, issue 1, 57-60

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.

Keywords: Gartner-Ellis; theorem; Large; deviations; theory (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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