Normal Approximations with Malliavin Calculus

From MaRDI portal
Publication:2891288

DOI10.1017/CBO9781139084659zbMath1266.60001OpenAlexW48692188MaRDI QIDQ2891288

Giovanni Peccati, Ivan Nourdin

Publication date: 15 June 2012

Full work available at URL: https://doi.org/10.1017/cbo9781139084659




Related Items (only showing first 100 items - show all)

Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noiseQuantitative stable limit theorems on the Wiener spaceA quantitative central limit theorem for the Euler-Poincaré characteristic of random spherical eigenfunctionsGeneralization of the Nualart-Peccati criterionRate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusionsParametric Stein operators and variance boundsAn Edgeworth expansion for functionals of Gaussian fields and its applicationsBerry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequencesFisher information and the fourth moment theoremClassical and free fourth moment theorems: universality and thresholdsMultivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimationConvergence in total variation to a mixture of Gaussian lawsNon-universality of nodal length distribution for arithmetic random wavesDiscretizing Malliavin calculusOn normal approximations for the two-sample problem on multidimensional toriBerry-Esseen type bound of a sequence \(\left\{\frac{X_N}{Y_N}\right\}\) and its applicationAsymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian modelOptimal Berry-Esseen bound for parameter estimation of SPDE with small noiseThe fourth moment theorem on the Poisson spaceWeak symmetric integrals with respect to the fractional Brownian motionFourth moment theorem and \(q\)-Brownian chaosPoisson approximations on the free Wigner chaosApproximating dependent rare eventsLeast squares estimator of fractional Ornstein-Uhlenbeck processes with periodic meanPoisson convergence on the free Poisson algebraDensity convergence in the Breuer-Major theorem for Gaussian stationary sequencesBounds for the normal approximation of the maximum likelihood estimator from \(m\)-dependent random variablesAsymptotic behavior of the Whittle estimator for the increments of a Rosenblatt processSquared chaotic random variables: new moment inequalities with applicationsDrift estimation with non-Gaussian noise using Malliavin calculusA Stein deficit for the logarithmic Sobolev inequalityA white noise approach to stochastic integration with respect to the Rosenblatt processEstimating self-similarity through complex variationsApproximate normality of high-energy hyperspherical eigenfunctionsWigner chaos and the fourth momentStein's method and approximating the quantum harmonic oscillatorCentral and non-central limit theorems in a free probability settingQuantitative CLTs for symmetric \(U\)-statistics using contractionsStructure of the third moment of the generalized Rosenblatt distributionFourth moment theorems on the Poisson space: analytic statements via product formulaeStein operators for variables form the third and fourth Wiener chaosesSensitivity of the Hermite rankInequalities for integrals of the modified Struve function of the first kind. II.First-order Euler scheme for SDEs driven by fractional Brownian motions: the rough caseRosenblatt Laplace motionConsistency of non-integrated depths for functional dataApproximation of stable law in Wasserstein-1 distance by Stein's methodWeak universality for a class of 3d stochastic reaction-diffusion modelsOn the limiting behaviour of needlets polyspectraParameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kindThe universality of homogeneous polynomial forms and critical limitsSecond-order matrix concentration inequalitiesParameter estimation for the Rosenblatt Ornstein-Uhlenbeck process with periodic meanA reduction principle for the critical values of random spherical harmonicsCentral limit theorem for functionals of a generalized self-similar Gaussian processRandom geometric complexes in the thermodynamic regimeOptimal Berry-Esseen bound for statistical estimations and its application to SPDEQuantitative central limit theorems for Mexican needlet coefficients on circular Poisson fieldsFourth moment theorems on the Poisson space in any dimensionThe Gamma Stein equation and noncentral de Jong theoremsEfficient strategy for the Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distributionEstimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic meanInequalities for integrals of modified Bessel functions and expressions involving themNormal approximation and almost sure central limit theorem for non-symmetric Rademacher functionalsTotal variation bounds for Gaussian functionalsA bound on the Wasserstein-2 distance between linear combinations of independent random variablesBehavior of the Hermite sheet with respect to the Hurst indexA new proof of central limit theorem for i.i.d. random variablesLarge deviations of empirical measures of diffusions in weighted topologiesInequalities for integrals of the modified Struve function of the first kindPseudo-binomial approximation to \((k_1, k_2)\)-runsFunctional approximations via Stein's method of exchangeable pairsA central limit theorem for the stochastic wave equation with fractional noiseAsymptotic development for the CLT in total variation distanceBounds for an integral of the modified Bessel function of the first kind and expressions involving itFunctional Cramér-Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processesLimiting behavior of large correlated Wishart matrices with chaotic entriesLimit theorems for integral functionals of Hermite-driven processesAn algebra of Stein operatorsTotal variation estimates in the Breuer-Major theoremNormal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilizationStein's method for asymmetric \(\alpha \)-stable distributions, with application to the stable CLTAsymptotic behavior of weighted power variations of fractional Brownian motion in Brownian timeCentral limit theorem for Lipschitz-Killing curvatures of excursion sets of Gaussian random fieldsOn almost sure convergence of random variables with finite chaos decompositionStable limit theorems on the Poisson spaceApproximation of Hilbert-valued gaussians on Dirichlet structuresMoments of Gaussian chaoses in Banach spacesStein's method of exchangeable pairs in multivariate functional approximationsSpatial ergodicity and central limit theorems for parabolic Anderson model with delta initial conditionEstimating drift parameters in a non-ergodic Gaussian Vasicek-type modelParameter estimation for discretely sampled stochastic heat equation driven by space-only noiseConvergence rate of CLT for the drift estimation of sub-fractional Ornstein-Uhlenbeck process of second kindModeling temporally uncorrelated components of complex-valued stationary processesGaussian fluctuation for Gaussian Wishart matrices of overall correlationStein's method for rough pathsRestriction of 3D arithmetic Laplace eigenfunctions to a planeRegularization lemmas and convergence in total variationStein characterizations for linear combinations of gamma random variablesHigh-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere




This page was built for publication: Normal Approximations with Malliavin Calculus