Functional inequalities for discrete gradients  
 and application to the geometric distribution

Aldéric Joulin; Nicolas Privault

Displaying similar documents to “Functional inequalities for discrete gradients and application to the geometric distribution”

The large deviation principle for certain series

Miguel A. Arcones (2010)

ESAIM: Probability and Statistics

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We study the large deviation principle for stochastic processes of the form ${\sum_{k = 1}^{\infty} x_{k} (t) ξ_{k} : t \in T}$ , where ${ξ_{k}}_{k = 1}^{\infty}$ is a sequence of i.i.d.r.v.'s with mean zero and $x_{k} (t) \in ℝ$ . We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity...

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

Jamal Najim (2010)

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...

Oscillations and concentrations in sequences of gradients

Agnieszka Kałamajska, Martin Kružík (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, ${\nabla u_{k}}$ , bounded in $L^{p} (Ω; ℝ^{m \times n})$ if and $Ω \subset ℝ^{n}$ is a bounded domain with the extension property in $W^{1, p}$ . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of are required and links with lower semicontinuity...

The nonlinear membrane model: a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We establish two new formulations of the membrane problem by working in the space of $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -Young measures and $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...