Comparison theorems for small deviations of random series.

Gao, F.; Hannig, J.; Torcaso, F.

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Moderate deviations for I.I.D. random variables

Peter Eichelsbacher, Matthias Löwe (2003)

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.

On the weak law of large numbers for normed weighted sums of i.i.d. random variables.

Adler, André, Rosalsky, Andrew (1991)

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Laws of large numbers for asymmetrical Cauchy random variables.

Adler, André (2007)

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On complete convergence for arrays of rowwise $ρ$ -mixing random variables and its applications.

Zhou, Xing-Cai, Lin, Jin-Guan (2010)

Journal of Inequalities and Applications [electronic only]

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

Roitershtein, Alexander (2005)

Electronic Communications in Probability [electronic only]

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An estimate of the essential norm of a composition operator from $F (p, q, s)$ to $ℬ^{α}$ in the unit ball.

Zeng, Hong-Gang, Zhou, Ze-Hua (2010)

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Gaussian scaling for the critical spread-out contact process above the upper critical dimension.

van der Hofstad, Remco, Sakai, Akira (2004)

Electronic Journal of Probability [electronic only]

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A limit theorem for functionals of a Poisson process

van Huu Nguyen (1979)

Commentationes Mathematicae Universitatis Carolinae

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New limiting distributions of maxima of independent random variables.

Graça Temido, M. (2003)

Portugaliae Mathematica. Nova Série

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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...