Corpus ID: 119147701

# Gaussian Approximations for Probability Measures on $\mathbf{R}^d$

@article{Lu2016GaussianAF,
title={Gaussian Approximations for Probability Measures on \$\mathbf\{R\}^d\$},
author={Y. Lu and A. Stuart and H. Weber},
journal={arXiv: Probability},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Probability
This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this divergence, from certain sets of Gaussian measures and Gaussian mixtures. The asymptotic behavior of such best approximations is then studied in the small parameter limit where the measure concentrates; this asymptotic behaviour is characterized using \$\Gamma… Expand
6 Citations

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