5 papers
Breuer-Major-Donsker invariance principle
Paul Mansanarez, Guillaume Poly, Guangqu Zheng
We prove a Breuer-Major-type Donsker's invariance principle for stationary Gaussian sequences under the natural \emph{finite-variance assumption} on the test function. This result,…
Non-separable graphs meet Ledoux's polynomials
Paul Mansanarez
In the pathbreaking article \cite{LED16}, an integral representation of the derivatives of entropy along the heat flow of a probability measure was established under suitable momen…
Edgeworth expansion on Wiener chaos
Paul Mansanarez, Guillaume Poly, Yvik Swan
Consider an element of the -th Wiener chaos $\WW_p$, and denote by $\prob_F$ its law. For a positive integer , let be the Radon measure with density…
Stein's method for Fréchet approximation: a regularly varying functions approach
Paul Mansanarez, Guillaume Poly, Yvik Swan
We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our…
Derivatives of entropy and the MMSE conjecture
Paul Mansanarez, Guillaume Poly, Yvik Swan
We investigate the entropy of a probability measure along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided th…