References of "Electronic Journal of Probability"
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See detailConcentration bounds for geometric Poisson functionals: logarithmic Sobolev inequalities revisited
Peccati, Giovanni UL; Bachmann, Sascha

in Electronic Journal of Probability (in press)

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See detailStein's method of exchangeable pairs in multivariate functional approximations
Döbler, Christian UL; Kasprzak, Mikolaj UL

in Electronic Journal of Probability (2021)

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See detailRadial processes for sub-Riemannian Brownian motions and applications
Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa et al

in Electronic Journal of Probability (2020), 25(paper no. 97), 1-17

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating ... [more ▼]

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. In the context of Sasakian foliations and H-type groups, one can push the analysis further, and taking advantage of the recently proved sub-Laplacian comparison theorems one can compare the radial processes for the sub-Riemannian distance to one-dimensional model diffusions. As a geometric application, we prove Cheng's type estimates for the Dirichlet eigenvalues of the sub-Riemannian metric balls, a result which seems to be new even in the Heisenberg group. [less ▲]

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See detailApproximation of Hilbert-valued Gaussians on Dirichlet structures
Bourguin, Solesne; Campese, Simon UL

in Electronic Journal of Probability (2020), 25

We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular ... [more ▼]

We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to the usual (non-quantitative) finite dimensional distribution convergence and tightness argument for proving functional convergence of stochastic processes. We also derive four moments bounds for Hilbert-valued random variables with possibly infinite chaos expansion, which include, as special cases, all finite-dimensional four moments results for Gaussian approximation in a diffusive context proved earlier by various authors. Our main ingredient is a combination of an infinite-dimensional version of Stein’s method as developed by Shih and the so-called Gamma calculus. As an application, rates of convergence for the functional Breuer-Major theorem are established. [less ▲]

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See detailA Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages
Basse-O'Connor, Andreas; Thäle, Christoph; Podolskij, Mark UL

in Electronic Journal of Probability (2020), 25(31), 131

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See detailQuantitative CLTs for symmetric U-statistics using contractions
Döbler, Christian UL; Peccati, Giovanni UL

in Electronic Journal of Probability (2019)

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See detailPhase singularities in complex arithmetic random waves
Dalmao, Federico; Nourdin, Ivan UL; Peccati, Giovanni UL et al

in Electronic Journal of Probability (2019), 24(71), 1-45

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See detailEvolution systems of measures and semigroup properties on evolving manifolds
Cheng, Li Juan UL; Thalmaier, Anton UL

in Electronic Journal of Probability (2018), 23(20), 1-27

An evolving Riemannian manifold (M,g_t)_{t\in I} consists of a smooth d-dimensional manifold M, equipped with a geometric flow g_t of complete Riemannian metrics, parametrized by I=(-\infty,T). Given an ... [more ▼]

An evolving Riemannian manifold (M,g_t)_{t\in I} consists of a smooth d-dimensional manifold M, equipped with a geometric flow g_t of complete Riemannian metrics, parametrized by I=(-\infty,T). Given an additional C^{1,1} family of vector fields (Z_t)_{t\in I} on M. We study the family of operators L_t=\Delta_t +Z_t where \Delta_t denotes the Laplacian with respect to the metric g_t. We first give sufficient conditions, in terms of space-time Lyapunov functions, for non-explosion of the diffusion generated by L_t, and for existence of evolution systems of probability measures associated to it. Coupling methods are used to establish uniqueness of the evolution systems under suitable curvature conditions. Adopting such a unique system of probability measures as reference measures, we characterize supercontractivity, hypercontractivity and ultraboundedness of the corresponding time-inhomogeneous semigroup. To this end, gradient estimates and a family of (super-)logarithmic Sobolev inequalities are established. [less ▲]

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See detailFourth moment theorems on The Poisson space in any dimension
Döbler, Christian UL; Vidotto, Anna UL; Zheng, Guangqu UL

in Electronic Journal of Probability (2018)

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See detailRecurrence and Transience of Frogs with Drift on Z^d
Döbler, Christian UL; Gantert, Nina; Höfelsauer, Thomas et al

in Electronic Journal of Probability (2018)

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See detailQuantitative de Jong theorems in any dimension
Döbler, Christian UL; Peccati, Giovanni UL

in Electronic Journal of Probability (2017), 22

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See detailAn iterative technique for bounding derivatives of solutions of Stein equations
Döbler, Christian UL; Gaunt, Robert E.; Vollmer, Sebastian J.

in Electronic Journal of Probability (2017), 22

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See detailStein's method of exchangeable pairs for the Beta distribution and generalizations
Döbler, Christian UL

in Electronic Journal of Probability (2015)

Detailed reference viewed: 166 (11 UL)
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See detailPortmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
Borguin, Solesne; Peccati, Giovanni UL

in Electronic Journal of Probability (2014), 19(Paper 66),

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See detailW1,+-interpolation of probability measures on graphs
Hillion, Erwan UL

in Electronic Journal of Probability (2014), 19

We generalize an equation introduced by Benamou and Brenier and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the ... [more ▼]

We generalize an equation introduced by Benamou and Brenier and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a nal distributions (f_0(x)), (f_1(x)), we prove the existence of a curve (f_t(x)) satisfying this Benamou-Brenier equation. We also show that such a curve can be described as a mixture of binomial distributions with respect to a coupling that is solution of a certain optimization problem. [less ▲]

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See detailStochastic flows on metric graphs
Hajri, Hatem UL; Raimond, Olivier

in Electronic Journal of Probability (2014)

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See detailAn Itô's type formula for the fractional Brownian motion in Brownian time
Nourdin, Ivan UL; Zeineddine, Raghid

in Electronic Journal of Probability (2014), 19(99), 1-15

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See detailAbsolute continuity and convergence of densities for random vectors on Wiener chaos
Nourdin, Ivan UL; Nualart, David; Poly, Guillaume Joseph UL et al

in Electronic Journal of Probability (2013), 18(22), 1--19

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See detailFine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs
Lachièze-Rey, Raphaël; Peccati, Giovanni UL

in Electronic Journal of Probability (2013), 18

Detailed reference viewed: 128 (1 UL)
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See detailStein's method and the multivariate CLT for traces of powers on the classical compact groups
Döbler, Christian UL; Stolz, Michael

in Electronic Journal of Probability (2011)

Detailed reference viewed: 58 (2 UL)