56 citations · 199 across the 30 of their papers we have counts for
25 papers · 1 filter
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…
Concentration of measure on spheres and related manifolds
Friedrich Götze, Holger Sambale
We study various generalizations of concentration of measure on the unit sphere, in particular by means of log-Sobolev inequalities. First, we show Sudakov-type concentration resul…
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…
Asymptotic Expansions and two-sided Bounds in Randomized Central Limit Theorems
S. G. Bobkov, G. P. Chistyakov, F. Götze
Lower and upper bounds are explored for the uniform (Kolmogorov) and -distances between the distributions of weighted sums of dependent summands and the normal law. The result…