exponential inequality
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Author(s):  
Michał Brzozowski

AbstractThe paper contains a study of weighted exponential inequalities for differentially subordinate martingales, under the assumption that the underlying weight satisfies Muckenhoupt’s condition $$A_{\infty }$$ A ∞ . The proof exploits certain functions enjoying appropriate size conditions and concavity. The martingales are adapted, uniformly integrable, and càdlàg - we do not assume any path-continuity restrictions. Because of this generality, we need to handle jump parts of processes which forces us to construct a Bellman function satisfying a stronger condition than local concavity. As a corollary, we will establish some new weighted $$L^p$$ L p estimates for differential subordinates of bounded martingales.





2021 ◽  
Vol 66 (3) ◽  
pp. 508-533
Author(s):  
Davide Giraudo ◽  
Davide Giraudo

Устанавливается экспоненциальное неравенство для вырожденных $U$-статистик порядка $r$, основанных на н.о.р. данных. Это неравенство позволяет оценить хвост максимума абсолютной величины $U$-статистики суммой двух членов: экспоненциального и второго члена, содержащего хвост $h(X_1,…,X_n)$. Также предлагается вариант неравенства для необязательно вырожденной $U$-статистики с симметричным ядром. Рассмотрены приложения к оценке скорости сходимости в законе больших чисел Марцинкевича и принципу инвариантности в гeльдеровом пространстве.





2019 ◽  
Vol 146 ◽  
pp. 65-69
Author(s):  
P. Hodara ◽  
P. Reynaud-Bouret


2018 ◽  
Vol 61 (4) ◽  
pp. 1607-1627
Author(s):  
Xin Deng ◽  
Xuejun Wang


2017 ◽  
Vol 101 (552) ◽  
pp. 470-475
Author(s):  
Nick Lord


Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 295-308
Author(s):  
Lulu Zheng ◽  
Xuejun Wang ◽  
Wenzhi Yang

In this paper, we present some results on the complete convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables by using the Rosenthal-type maximal inequality, Kolmogorov exponential inequality and the truncation method. The results obtained in the paper extend the corresponding ones for weighted sums of negatively associated random variables with identical distribution to the case of arrays of rowwise NSD random variables without identical distribution.





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