A Cramér type theorem for weighted random variables.

Najim, Jamal

Displaying similar documents to “A Cramér type theorem for weighted random variables.”

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

Jamal Najim (2005)

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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...

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Asymptotic behavior of moment sequences.

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Conditional principles for random weighted measures

Nathael Gozlan (2005)

ESAIM: Probability and Statistics

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In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form $L_{n} = \frac{1}{n} \sum_{i = 1}^{n} Z_{i} δ_{x_{i}^{n}}$ , ${(Z_{i})}_{i}$ being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.

Large deviations for the empirical measures of reflecting Brownian motion and related constrained processes in $ℝ_{+}$ .

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Gaussian limits for random geometric measures.

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A relaxation result in BV for integral functionals with discontinuous integrands

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ESAIM: Control, Optimisation and Calculus of Variations

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We prove a relaxation theorem in BV for a non coercive functional with linear growth. No continuity of the integrand with respect to the spatial variable is assumed.