The functional moderate deviations for Harris recurrent Markov chains and applications

Xia Chen; Arnaud Guillin

Displaying similar documents to “The functional moderate deviations for Harris recurrent Markov chains and applications”

Moderate deviations for I.I.D. random variables

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ESAIM: Probability and Statistics

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We derive necessary and sufficient conditions for a sum of i.i.d. random variables $\sum_{i = 1}^{n} X_{i} / b_{n}$ – where $\frac{b_{n}}{n} ↓ 0$ , but $\frac{b_{n}}{\sqrt{n}} ↑ \infty$ – to satisfy a moderate deviations principle. Moreover we show that this equivalence is a typical moderate deviations phenomenon. It is not true in a large deviations regime.

Comparison theorems for small deviations of random series.

Gao, F., Hannig, J., Torcaso, F. (2003)

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On an infinite series for ${(1 + 1 / x)}^{x}$ and its application.

Chen, Hongwei (2002)

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Density estimation for one-dimensional dynamical systems

Clémentine Prieur (2001)

ESAIM: Probability and Statistics

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In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.

Complete convergence for negatively dependent random variables.

Amini, D. M., Bozorgnia, A. (2003)

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A log-scale limit theorem for one-dimensional random walks in random environments.

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Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment

Jonathon Peterson (2009)

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

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We consider a nearest-neighbor, one-dimensional random walk { } in a random i.i.d. environment, in the regime where the walk is transient with speed >0 and there exists an ∈(1, 2) such that the annealed law of ( − ) converges to a stable law of parameter . Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular we show that there exist sequences...

Multidimensional limit theorems for smoothed extreme value estimates of point processes boundaries

Ludovic Menneteau (2008)

ESAIM: Probability and Statistics

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In this paper, we give sufficient conditions to establish central limit theorems and moderate deviation principle for a class of support estimates of empirical and Poisson point processes. The considered estimates are obtained by smoothing some bias corrected extreme values of the point process. We show how the smoothing permits to obtain Gaussian asymptotic limits and therefore pointwise confidence intervals. Some unidimensional and multidimensional examples are provided. ...