| Issue |
ESAIM: PS
Volume 23, 2019
|
|
|---|---|---|
| Page(s) | 922 - 946 | |
| DOI | https://doi.org/10.1051/ps/2019016 | |
| Published online | 03 January 2020 | |
Deviation inequalities for Banach space valued martingales differences sequences and random fields*
Ruhr-Universität Bochum Fakultät für Mathematik Universitätsstraße 150,
44780
Bochum, Germany.
** Corresponding author: Davide.Giraudo@rub.de
Received:
21
December
2017
Accepted:
8
July
2019
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of an orthomartingale differences random field. These inequalities can be used to give rates for linear regression and the law of large numbers.
Mathematics Subject Classification: 60B12 / 60G42 / 60G48 / 60G60
Key words: Martingales / random fields / orthomartingales / deviation inequalities / complete convergence
The author would like to thank Christophe Cuny for giving the statement and proof of Lemma 2.5 and Proposition 2.6, and the referees, for the improvement of the condition of stochastic domination and the application to regression model, and for all the comments which improved the readability of the paper.
© EDP Sciences, SMAI 2020
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