Transportation cost-information inequalities and applications to random dynamical systems and diffusions

By Hacène Djellout, Arnaud Guillin, Liming Wu. 2004

288 citations recorded by the source corpus.

We first give a characterization of the L1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/579660ef2723f2a6aaf048c2ccdd0c1262912cf4

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions (2021, methodology): “2, uses a known method based on Girsanov’s theorem [17, 75, 59] to deduce that μ satisfies a quadratic transport inequality with respect to the sup-norm; see also [3, 2] for recent results on quadratic transport inequalities for SDEs with irregular coefficients, which may be useful in deriving addit”
Hamilton Jacobi equations on metric spaces and transport-entropy inequalities (2012, background): “Let f be a bounded and continuous function on X and k : (a, b) → (0,+∞) be a function of class C1 defined on an open interval (a, b) ⊂ (0,∞) and such that k′(t) 6= 0 for all t. Define H(t) = 1 k(t) log ( ∫ ek(t)Qtf dµ ) and K(t) = 1 k(t) log ( ∫ ek(t)Ptf dµ ) , t ∈ (a, b).”
From the master equation to mean field game limit theory: Large deviations and concentration of measure (2018, background): “The proofs rely on transport inequalities, crucially using a result of [21].”
A characterization of dimension free concentration in terms of transportation inequalities (2008, background): “More precisely, one has the following theorem due to Djellout, Guillin and Wu [16].”
Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, unknown): “It has been proven [7, 14, 8] that T1 is equivalent to the existence of a square-exponential moment: in other words, a reference measure μ satisfies T1 if and only if there is α > 0 such that ∫ e 2 dμ(x) < +∞ for some (and thus any) y ∈ X.”
A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature (2009, background): “…on (1.1), provided the stationary distribution π satisfies some functional inequalities such as Poincaré, log-Sobolev or transportation-type inequalities; see, for instance, the recent articles of Cattiaux and Guillin (2008), Djellout et al. (2004), Gourcy and Wu (2006) or Guillin et al. (2009).”
Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion (2012, methodology): “In [8], the authors have linked C with the above exponential moment in the following way: C ≤ 2 δ sup k≥1 ( (k!)(2) (2k)! ∫”
Transport Inequalities. A Survey (2010, background): “Djellout, Guillin and Wu [37] were the first ones to notice that the inequality T1 is equivalent to the integrability condition ∫ X×X e bd(x,y)2 dμ(x)dμ(y) < +∞.”