A new modified logarithmic Sobolev inequality for Poisson point processes and several applications

By Liming Wu. 2000

184 citations recorded by the source corpus.

Subfields: Applied Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3e414e65fc1a6bb91a62c38c656f9a95ff7fbd39

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In Applied Mathematics

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In Statistics and Probability

Citations in the corpus

Concentration and deviation inequalities in infinite dimensions via covariance representations (2002, methodology): “Here we tackle the infinite dimensional case with a similar method, recovering the results recently obtained in [2], [6], using (modified) logarithmic Sobolev inequalities, and also the stronger results of [30] obtained from sharp logarithmic Sobolev inequalities, cf.”
Quantitative results on the corrector equation in stochastic homogenization (2014, background): “In the case of the Poisson point process, a corresponding covariance estimate holds as well and is known as the Harris–FKG inequality, see [25, 21].”
Poisson process Fock space representation, chaos expansion and covariance inequalities (2009, methodology): “8) was previously derived by [43] using an explicit martingale representation.”
Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales (2009, methodology): “+qE [f ] log ( 1− p df E [f ] ) − qpdf log f(−1) ≤ pqdf log f(1)− pqdf log f(−1) = pqE [dfd log f ] , which, by tensorization, recovers the following L(1) inequality of [49], [31], and proved in [155] in the Poisson case.”
Normal approximation on Poisson spaces: Mehler’s formula, second order Poincaré inequalities and stabilization (2014, background): “The Poincaré inequality (see [26, 55] and the references therein) states that the variance of a square-integrable Poisson functional F can be bounded as VarF ≤ E ∫”
Fractional Poincaré inequalities for general measures (2009, unknown): “For instance it was proved by Wu [Wu00] and Chafa¨ı [Cha04] that (see also the use of this inequality in [GI08]) with and D Φ is the so-called Bregman distance associated to Φ: where Φ is some well-suited functional with convexity properties, σ the matrix of diﬀusion of the process, µ a rather…”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, background): “It is well known that cP = 1 but the log-Sobolev inequality does not hold ([53]).”
Central limit theorems for $U$-statistics of Poisson point processes (2011, background): “Yet only in the last years prominent contributions produced a deep theory which most probably will have a strong impact on modern theory and applications of Poisson point processes; see, for example, Houdre and Perez-Abreu [12], Last and Penrose [19], Nualart and Vives [25] and Wu [38].”
Entropies, convexity, and functional inequalities (2002, methodology): “Moreover, it is bivariate convex when Φ(x) = x logx or Φ(x) = x 2 , as observed in the pretty paper [ Wu00 ].”
On contraction properties of Markov kernels (2003, methodology): “This fact was already used by Wu [ 16 ] to study Poisson point processes.”
Entropies, convexity, and functional inequalities : On Phi-entropies and Phi-Sobolev inequalities (2004, methodology): “Moreover, it is bivariate convex when Φ(x) = x logx or Φ(x) = x 2 , as observed in the pretty paper [ Wu00 ].”
Stochastic analysis for Poisson processes (2014, background): “The following general version is taken from [32].”