Open AccessJournal Article
Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants
TLDR
In this paper, a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field is considered, and it is assumed that E(F 4 4 ) is a Gaussian distribution.Abstract:
Let fFn : n > 1g be a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that E(F 4read more
Citations
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Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Journal ArticleDOI
The optimal fourth moment theorem
Ivan Nourdin,Giovanni Peccati +1 more
TL;DR: In this article, the exact rates of convergence in total variation associated with Nualart and Peccati's "fourth moment theorem" were derived. But the convergence rate of the fourth moment theorem is not known.
Journal ArticleDOI
Malliavin-Stein method for variance-gamma approximation on Wiener space
TL;DR: In this paper, the authors combine Malliavin calculus with Stein's method to derive bounds for the Variance-Gamma approximation of functionals of isonormal Gaussian processes, in particular of random variables living inside a fixed Wiener chaos induced by such a process.
Journal ArticleDOI
Optimal rates for parameter estimation of stationary Gaussian processes
Khalifa Es-Sebaiy,Frederi Viens +1 more
TL;DR: In this article, the convergence rate of partial sums of polynomial functionals of general stationary and asymptotically stationary Gaussian sequences was studied using tools from analysis on Wiener space.
Book ChapterDOI
Lectures on Gaussian Approximations with Malliavin Calculus
TL;DR: In a seminal paper of 2005, Nualart and Peccati as discussed by the authors showed that convergence in distribution to the standard normal law is equivalent to convergence of just the fourth moment.
References
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Book
The Malliavin Calculus and Related Topics
TL;DR: The Malliavin calculus as mentioned in this paper is an infinite-dimensional differential calculus on a Gaussian space, originally developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis.
MonographDOI
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
TL;DR: In this paper, the authors introduce sample path properties such as boundedness, continuity, and oscillations, as well as integrability, and absolute continuity of the path in the real line.
Book
Stochastic Analysis
TL;DR: These are lecture notes from the lessons given in the fall 2010 at Harvard University, based on distinct references, and Chapter 3 is adapted from the remarkable lecture notes by Jean François Le Gall, in French.