Nonconventional large deviations theorems

Yuri Kifer, Srinivasa Varadhan

Research output: Contribution to journalArticle

Abstract

We obtain large deviations theorems for both discrete time expressions of the form ∑n=1 N F(X(q1(n)),..., X(qℓ(n))) and similar expressions of the form ∫0 T F(X(q1(t)),..., X(qℓ(t))) dt in continuous time. Here X(n),n≥ 0 or X(t), t≥ 0 is a Markov process satisfying Doeblin's condition, F is a bounded continuous function and qi(n) = in for i ≤ k while for i>k they are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when qi's are polynomials of increasing degrees. Applications to some types of dynamical systems such as mixing subshifts of finite type and hyperbolic and expanding transformations will be obtained, as well.

Original languageEnglish (US)
Pages (from-to)197-224
Number of pages28
JournalProbability Theory and Related Fields
Volume158
Issue number1-2
DOIs
StatePublished - 2014

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Large Deviations
Subshift
Integer
Finite Type
Growth Conditions
Theorem
Markov Process
Continuous Time
Continuous Function
Discrete-time
Dynamical system
Polynomial
Form
Large deviations
Markov process
Continuous time
Dynamical systems
Polynomials

Keywords

  • Hyperbolic diffeomorphisms
  • Large deviations
  • Markov processes
  • Nonconventional averages

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Statistics, Probability and Uncertainty

Cite this

Nonconventional large deviations theorems. / Kifer, Yuri; Varadhan, Srinivasa.

In: Probability Theory and Related Fields, Vol. 158, No. 1-2, 2014, p. 197-224.

Research output: Contribution to journalArticle

Kifer, Yuri ; Varadhan, Srinivasa. / Nonconventional large deviations theorems. In: Probability Theory and Related Fields. 2014 ; Vol. 158, No. 1-2. pp. 197-224.
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