2017/01/11 by Yacine Barhoumi-Andréani, Barhoumi-Andréani, Yacine
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1701.03086
arxiv created 2017/01/11 · arxiv updated 2017/01/12
Stein's method allows to prove distributional convergence of a sequence of random variables and to quantify it with respect to a given metric such as Kolmogorov's (a Berry-Esséen type theorem). Mod-* convergence quantifies the convergence of a sequence of random variables to a given distribution in a sense unusual in probability theory, a priori unrelated to a metric on probability measures. This article gives a connection between these two notions. It shows that mod-* convergence can be understood as a higher order approximation in distribution when the limiting function is integrable and proves a refined Berry-Esséen type theorem for sequences converging in the mod-Gaussian sense.