Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula
From MaRDI portal
Publication:2312685
DOI10.1007/s00440-018-0874-5zbMath1479.60003arXiv1801.07815OpenAlexW2887260164MaRDI QIDQ2312685
Lihu Xu, Xiao Fang, Qui-Man Shao
Publication date: 17 July 2019
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.07815
Stochastic calculus of variations and the Malliavin calculus (60H07) Convergence of probability measures (60B10)
Related Items
Approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equations ⋮ Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels ⋮ Non-integrable stable approximation by Stein's method ⋮ Central limit theorem and self-normalized Cramér-type moderate deviation for Euler-Maruyama scheme ⋮ The Prelimit Generator Comparison Approach of Stein’s Method ⋮ A kernel bound for non-symmetric stable distribution and its applications ⋮ First-order covariance inequalities via Stein's method ⋮ Stein's method for functions of multivariate normal random variables ⋮ Donsker's theorem in Wasserstein-1 distance ⋮ A probability approximation framework: Markov process approach ⋮ Using Stein's method to analyze Euler-Maruyama approximations of regime-switching jump diffusion processes ⋮ Stein's method meets computational statistics: a review of some recent developments ⋮ Stein's density method for multivariate continuous distributions ⋮ Approximation of the invariant measure of stable SDEs by an Euler-Maruyama scheme ⋮ Transportation onto log-Lipschitz perturbations ⋮ Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs ⋮ A diffusion approach to Stein's method on Riemannian manifolds ⋮ Unnamed Item ⋮ Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator ⋮ Correction to: Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multivariate Stein factors for a class of strongly log-concave distributions
- Reflection couplings and contraction rates for diffusions
- Diffusion models and steady-state approximations for exponentially ergodic Markovian queues
- Gradient estimates for SDEs driven by multiplicative Lévy noise
- Stein's method for steady-state diffusion approximations of \(\mathrm{M}/\mathrm{Ph}/n+\mathrm{M}\) systems
- Identifying the limiting distribution by a general approach of Stein's method
- Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model
- Berry-Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances
- On the rate of convergence in the multivariate CLT
- Stein's method on Wiener chaos
- A note on the exchangeability condition in Stein's method
- Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
- Multivariate normal approximation using Stein's method and Malliavin calculus
- Formulae for the derivatives of heat semigroups
- Exponential convergence of Langevin distributions and their discrete approximations
- A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
- Exponential and uniform ergodicity of Markov processes
- The CLT in high dimensions: quantitative bounds via martingale embedding
- Measuring sample quality with diffusions
- High-dimensional Bayesian inference via the unadjusted Langevin algorithm
- Stein's method, logarithmic Sobolev and transport inequalities
- Characterization of the convergence in total variation and extension of the fourth moment theorem to invariant measures of diffusions
- A high-dimensional CLT in \(\mathcal {W}_2\) distance with near optimal convergence rate
- Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
- Normal Approximations with Malliavin Calculus
- On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
- Quantitative Stability of the Entropy Power Inequality
- Multivariate normal approximations by Stein's method and size bias couplings
- A Lyapunov-type Bound in Rd
- Theoretical Guarantees for Approximate Sampling from Smooth and Log-Concave Densities
- Second order PDE's in finite and infinite dimension
- Elliptic operators on \(\mathbb{R}^d\) with unbounded coefficients