Poissonization Inequalities for Sums of Independent Random Variables in Banach Spaces with Applications to Empirical Processes

Author:

Borisov Igor1ORCID

Affiliation:

1. Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia

Abstract

Inequalities are obtained which connect the probability tails and moments of functions of the nth partial sums of independent random variables taking values in a separable Banach space and those for the accompanying infinitely divisible laws. Some applications to empirical processes are studied.

Funder

Basic Research Program of the Siberian Branch of the Russian Academy of Sciences

Publisher

MDPI AG

Reference35 articles.

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4. Prokhorov, Y.V. (1962, January 5–14). Extremal problems in limit theorems. Proceedings of the 6th USSR Conference on Probability Theory and Mathematical Statistics, Vilnius, Lithuania. (In Russian).

5. Exact exponential bounds for sums of independent random variables;Pinelis;Theory Probab. Appl.,1989

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