Large Deviations from the Almost Everywhere Central Limit Theorem

Peter March () and Timo Seppäläinen ()
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Peter March: Ohio State University
Timo Seppäläinen: Iowa State University

Journal of Theoretical Probability, 1997, vol. 10, issue 4, 935-965

Abstract: Abstract We prove large deviation principles for the almost everywhere central limit theorem, assuming that the i.i.d. summands have finite moments of all orders. The level 3 rate function is a specific entropy relative to Wiener measure and the level 2 rate the Donsker-Varadhan entropy of the Ornstein-Uhlenbeck process. In particular, the rate functions are independent of the particular distribution of the i.i.d. process under study. We deduce these results from a large deviation theory for Brownian motion via Skorokhod's representation of random walk as Brownian motion evaluated at random times. The results for Brownian motion come from the well-known large deviation theory of the Ornstein-Uhlenbeck process, by a mapping between the two processes.

Keywords: Large deviations; almost everywhere central limit theorem; Brownian motion (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1022614700678

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