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Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 2, Pages 209–227 (Mi tvp5188)  

Exponential inequalities for the distributions of canonical multiple partial sum processes

I. S. Borisovab, A. A. Bystrovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: Exponential inequalities are obtained for the distribution tail of the sup-norm of a multiple partial sum process with canonical bounded kernel based on independent and weakly dependent observations. The exponent obtained has the correct order.

Keywords: exponential inequalities, canonical $U$- and $V$-statistics, multiple orthogonal series.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00074-a
Siberian Branch of Russian Academy of Sciences 0314-2016-0008
This work was partially supported by the Russian Foundation for Basic Research (grant 18-01-00074-a) and the Program of Fundamental Scientific Research of SB RAS (project 0314-2016-0008).


DOI: https://doi.org/10.4213/tvp5188

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English version:
Theory of Probability and its Applications, 2019, 64:2, 171–185

Bibliographic databases:

Received: 26.03.2018
Revised: 03.06.2018
Accepted:21.06.2018

Citation: I. S. Borisov, A. A. Bystrov, “Exponential inequalities for the distributions of canonical multiple partial sum processes”, Teor. Veroyatnost. i Primenen., 64:2 (2019), 209–227; Theory Probab. Appl., 64:2 (2019), 171–185

Citation in format AMSBIB
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