On existence and uniqueness of univariate Stein kernels

Christian Döbler

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arXiv · 2502.03910

On existence and uniqueness of univariate Stein kernels

Christian Döbler

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Abstract

We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central limit theorem with optimal rate $n^{-1/2}$ in total variation distance for i.i.d. random variables whose distribution belongs to that class.

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Christian Döbler. 2025-02-06. On existence and uniqueness of univariate Stein kernels. https://arxiv.org/abs/2502.03910

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