5 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…
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.
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…