Large Deviations from the Almost Everywhere Central Limit Theorem

Peter March, Timo Seppäläinen

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)935-965
Number of pages31
JournalJournal of Theoretical Probability
Volume10
Issue number4
DOIs
StatePublished - Jan 1 1997

Fingerprint

Large Deviations
Central limit theorem
Large Deviation Theory
Brownian motion
Ornstein-Uhlenbeck Process
Rate Function
Wiener Measure
Large Deviation Principle
Relative Entropy
Deduce
Random walk
Entropy
Moment
Large deviations
Ornstein-Uhlenbeck process

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

  • Almost everywhere central limit theorem
  • Brownian motion
  • Large deviations

Cite this

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Large Deviations from the Almost Everywhere Central Limit Theorem. / March, Peter; Seppäläinen, Timo.

In: Journal of Theoretical Probability, Vol. 10, No. 4, 01.01.1997, p. 935-965.

Research output: Contribution to journalArticle

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