About the Lindeberg method for strongly mixing sequences

Emmanuel Rio

Displaying similar documents to “About the Lindeberg method for strongly mixing sequences”

Finite width for a random stationary interface.

Mueller, C., Tribe, R. (1997)

Electronic Journal of Probability [electronic only]

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$L^{1}$ -norm of infinitely divisible random vectors and certain stochastic integrals.

Marcus, Michael B., Rosiński, Jan (2001)

Electronic Communications in Probability [electronic only]

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On the approximation of an integral by a sum of random variables.

Einmahl, John H.J., Van Zuijlen, Martien C.A. (1998)

Journal of Applied Mathematics and Stochastic Analysis

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Complete $q$ -order moment convergence of moving average processes under $ϕ$ -mixing assumptions

Xing-Cai Zhou, Jin-Guan Lin (2014)

Applications of Mathematics

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Let ${Y_{i}, - \infty < i < \infty}$ be a doubly infinite sequence of identically distributed $ϕ$ -mixing random variables, and ${a_{i}, - \infty < i < \infty}$ an absolutely summable sequence of real numbers. We prove the complete $q$ -order moment convergence for the partial sums of moving average processes $\{X_{n} = \sum_{i = - \infty}^{\infty} a_{i} Y_{i + n}, n \geq 1\}$ based on the sequence ${Y_{i}, - \infty < i < \infty}$ of $ϕ$ -mixing random variables under some suitable conditions. These results generalize and complement earlier results.

A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit

Natalie Grunewald, Felix Otto, Cédric Villani, Maria G. Westdickenberg (2009)

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

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We consider the coarse-graining of a lattice system with continuous spin variable. In the first part, two abstract results are established: sufficient conditions for a logarithmic Sobolev inequality with constants independent of the dimension (Theorem 3) and sufficient conditions for convergence to the hydrodynamic limit (Theorem 8). In the second part, we use the abstract results to treat a specific example, namely the Kawasaki dynamics with Ginzburg–Landau-type potential.

Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers

Jamal Najim (2005)

ESAIM: Probability and Statistics

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A Large Deviation Principle (LDP) is proved for the family $\frac{1}{n} \sum_{1}^{n} 𝐟 (x_{i}^{n}) \cdot Z_{i}^{n}$ where the deterministic probability measure $\frac{1}{n} \sum_{1}^{n} δ_{x_{i}^{n}}$ converges weakly to a probability measure $R$ and ${(Z_{i}^{n})}_{i \in ℕ}$ are $ℝ^{d}$ -valued independent random variables whose distribution depends on $x_{i}^{n}$ and satisfies the following exponential moments condition: $sup_{i, n} 𝔼 e^{α^{*} | Z_{i}^{n} |} < + \infty forsome 0 < α^{*} < + \infty .$ In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Note on Dispersion of Xalpha

Dragan Banjević, D. Bratičević (1983)

Publications de l'Institut Mathématique

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Convergence of stopped sums of weakly dependent random variables.

Peligrad, Magda (1999)

Electronic Journal of Probability [electronic only]

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