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Large deviations for generic stationary processes

Emmanuel Lesigne, Dalibor Volný (2000)

Colloquium Mathematicae

Let (Ω,A,μ,T) be a measure preserving dynamical system. The speed of convergence in probability in the ergodic theorem for a generic function on Ω is arbitrarily slow.

Limit theorems for stationary Markov processes with L2-spectral gap

Déborah Ferré, Loïc Hervé, James Ledoux (2012)

Annales de l'I.H.P. Probabilités et statistiques

Let ( X t , Y t ) t 𝕋 be a discrete or continuous-time Markov process with state space 𝕏 × d where 𝕏 is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ( X t , Y t ) t 𝕋 is assumed to be a Markov additive process. In particular, this implies that the first component ( X t ) t 𝕋 is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ( Y t ) t 𝕋 is shown to satisfy the...

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