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Creators/Authors contains: "Götze, Friedrich"

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  1. ; (, Journal of Functional Analysis)
    The paper is devoted to the investigation of Esscher’s transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation for normalized sums of i.i.d. random vectors in terms of the Rényi divergence of infinite order, extending recent one dimensional results. 
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    Free, publicly-accessible full text available September 1, 2026
  2. ; (, Lithuanian mathematical journal)
    Berry–Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities. 
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    Free, publicly-accessible full text available March 20, 2026
  3. ; (, The Annals of Probability)
    For normalized sums Zn of i.i.d. random variables, we explore necessary and sufficient conditions, which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities pn of Zn, this is a strengthened variant of the local limit theorem taking the form sup (pn(x)− ϕ(x))/ϕ(x)→0 as n→∞. 
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    Free, publicly-accessible full text available March 1, 2026
  4. ; (, Probability Surveys)
    We give an overview of various results and methods related to information-theoretic distances of Rényi type in the light of their applications to the central limit theorem (CLT). The first part (Sections 1–9) is devoted to the total variation and the Kullback-Leibler distance (relative entropy). In the second part (Sections 10–15) we discuss general properties of Rényi and Tsall is divergences of order alpha > 1, and then in the third part (Sections 16–21) we turn to the CLT and non-uniform local limit theorems with respect to these strong distances. In the fourth part (Sections 22–31), we discuss recent results on strictly subgaussian distributions and describe necessary and sufficient conditions which ensure the validity of the CLT with respect to the Rényi divergence of infinite order. 
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  5. ; ; (, Lithuanian Mathematical Journal)
    We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).We also discuss related quantitative bounds for characteristic functions and Laplace transforms. 
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