An algebra of Stein operators

DOI10.1016/j.jmaa.2018.09.015zbMath1410.60032arXiv1604.06819OpenAlexW2890309407MaRDI QIDQ1798993

Robert E. Gaunt, Yvik Swan, Guillaume Mijoule

Publication date: 18 October 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.06819

zbMATH Keywords

Stein's methodStein operatorsvariance-gamma distributionproduct distributions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items

Stein’s method and the distribution of the product of zero mean correlated normal random variables, Stein's method for functions of multivariate normal random variables, The basic distributional theory for the product of zero mean correlated normal random variables, Unnamed Item, Stein’s method of normal approximation for dynamical systems, Stein operators for variables form the third and fourth Wiener chaoses, Malliavin-Stein method: a survey of some recent developments, Some new Stein operators for product distributions, Stein characterizations for linear combinations of gamma random variables, On algebraic Stein operators for Gaussian polynomials, New error bounds for Laplace approximationviaStein’s method

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stein's method for invariant measures of diffusions via Malliavin calculus
• Fundamentals of Stein's method
• Stein's method for comparison of univariate distributions
• Stein's method for dependent random variables occuring in statistical mechanics
• Generalized gamma approximation with rates for urns, walks and trees
• Stein's method of exchangeable pairs for the Beta distribution and generalizations
• Malliavin-Stein method for variance-gamma approximation on Wiener space
• Poisson approximation for dependent trials
• Closed form summation for classical distributions: variations on a theme of de Moivre
• Products of normal, beta and gamma random variables: Stein operators and distributional theory
• An iterative technique for bounding derivatives of solutions of Stein equations
• A probabilistic proof of some integral formulas involving the Meijer \(G\)-function
• Degree asymptotics with rates for preferential attachment random graphs
• Entropy and the fourth moment phenomenon
• On Stein's method for products of normal random variables and zero bias couplings
• Variance-gamma approximation via Stein's method
• Characterizations of GIG laws: a survey
• The special functions and their approximations. Vol. I, II
• Normal Approximations with Malliavin Calculus
• Stein's method and the Laplace distribution
• Two new proofs of the Erdös–Kac Theorem, with bound on the rate of convergence, by Stein's method for distributional approximations
• Normal Variance-Mean Mixtures and z Distributions
• A Stein characterisation of the generalized hyperbolic distribution
• On perturbations of Stein operator
• Stein's Method for the Beta Distribution and the Pólya-Eggenberger Urn
• The Distribution of Products of Independent Random Variables
• The Distribution of Products of Beta, Gamma and Gaussian Random Variables
• Orthogonal polynomials in Stein's method