Normal Approximations with Malliavin Calculus: From Stein's Method to Universality

By Ivan Nourdin, Giovanni Peccati. 2012

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Citations in the corpus

Stein's method for comparison of univariate distributions (2014, methodology): “Indeed [65, 66, 68] (among others) refer to τ as the “Stein factor” despite the fact that this term also refers to the bounds on the solutions of the Stein equations, see [81, 23, 7].”
Convergence in total variation on Wiener chaos (2012, background): “(For an overview of the existing literature, we refer the reader to the book [16], to the survey [14] or to the constantly updated web page [13].”
Approximation of stable law in Wasserstein-1 distance by Stein’s method (2017, methodology): “Nowadays, Stein’s method has been extended and refined by many authors and become a very important tool for getting bounds of measure approximations, see [6, 10, 14, 22, 24, 29, 39, 46, 26, 27, 28, 33, 42, 43, 44, 47].”
The optimal fourth moment theorem (2013, background): “MSC 2010: 60F05; 60G15; 60H07”
On Stein's method for products of normal random variables and zero bias couplings (2013, methodology): “Indeed, the Malliavin-Stein method (see Nourdin and Peccati [32] for an introduction), that was originally developed for Gaussian approximation, is applicable to a wide class of laws; see, for example, Eden and Viens [11] and Eden and Viquez [12].”
Stein kernels and moment maps (2018, background): “It has applications to central limit theorems [30], concentration inequalities [33, 25, 36] and random matrix theory [10].”
Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean (2015, unknown): “[7]).”
Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter (2017, background): “The map Im provides a linear isometry between H m(equipped with the norm 1 √ m! || · ||H⊗m) and Hm (equipped with L2(Ω) norm) (see [20], Theorem 2.”
Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, background): “3 in [21]), to show the convergence in law of (ΘL,BL), it suffices to show the convergence of each component of (ΘL,BL) to the correspondent component of (WL,BL) and the convergence of the covariance matrix.”
Optimal rates for parameter estimation of stationary Gaussian processes (2016, methodology): “The study of the asymptotic properties of the estimator is based on certain criteria formulated in terms of the Malliavin calculus (see [24]).”
Gaussian fluctuations for the stochastic heat equation with colored noise (2019, background): “3) where D is the Malliavin derivative, L is the pseudo-inverse of the OrnsteinUhlenbeck operator and 〈·, ·〉H denotes the inner product in the Hilbert space H associated with the covariance of W ; see also the monograph [10].”
High-dimensional central limit theorems by Stein’s method (2020, methodology): “1 is also interesting in the context of the so-called Malliavin-Stein method (see Nourdin and Peccati (2012) for an exposition of this topic). For simplicity, we focus on the case that the coordinates of W are multiple Wiener-Itô integrals with common orders. We refer to Nourdin and Peccati (2012) f”
Absolute continuity and convergence of densities for random vectors on Wiener chaos (2012, background): “We refer the reader to the books [10, 13] for further details.”