7 citations · 14 across the 13 of their papers we have counts for
10 papers · 1 filter
A Quantitative Cramér-Wold Theorem for Zolotarev Distances
Sergey G. Bobkov, Friedrich Götze
An upper bound for Zolotarev distances between probability measures on multidimensional Euclidean spaces is given in terms of similar distances between one dimensional projections.
Quantified Cramér-Wold Continuity Theorem for the Kantorovich Transport Distance
Sergey G. Bobkov, Friedrich Götze
An upper bound for the Kantorovich transport distance between probability measures on multidimensional Euclidean spaces is given in terms of transport distances between one dimensi…
Berry-Esseen bounds in local limit theorems
Sergey Bobkov, Friedrich Götze
Berry-Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities.
Esscher Transform and the Central Limit Theorem
Sergey Bobkov, Friedrich Götze
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,…
Central Limit Theorem for Rényi Divergence of Infinite Order
Sergey G. Bobkov, Friedrich Götze
For normalized sums of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the Rényi divergence o…
Rényi divergence and the central limit theorem
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore properties of the and more general Rényi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to…
Stability of Cramer's Characterization of Normal Laws in Information Distances
S. G. Bobkov, G. P. Chistyakov, F. Götze
Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer's theorem with respect to relative entropy and F…
Regularized Distributions and Entropic Stability of Cramer's Characterization of the Normal Law
S. G. Bobkov, G. P. Chistyakov, F. Götze
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distanc…
Second order concentration on the sphere
S. G. Bobkov, G. P. Chistyakov, F. Götze
Sharpened forms of the concentration of measure phenomenon for classes of functions on the sphere are developed in terms of Hessians of these functions.
Fisher information and convergence to stable laws
S. G. Bobkov, G. P. Chistyakov, F. Götze
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.