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## Studia Mathematica

2011 | 205 | 2 | 171-200
Tytuł artykułu

### Disjointification of martingale differences and conditionally independent random variables with some applications

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Języki publikacji
EN
Abstrakty
EN
Disjointification inequalities are proven for arbitrary martingale difference sequences and conditionally independent random variables of the form ${f_{k}(s)x_{k}(t)}_{k=1}ⁿ$, where $f_{k}$'s are independent and x_{k}'s are arbitrary random variables from a symmetric space X on [0,1]. The main results show that the form of these inequalities depends on which side of L₂ the space X lies on. The disjointification inequalities obtained allow us to compare norms of sums of martingale differences and non-negative random variables with the norms of sums of their independent copies. The latter results can be treated as an extension of the modular inequalities proved earlier by de la Peña and Hitczenko to the setting of symmetric spaces. Moreover, using these results simplifies the proofs of some modular inequalities.
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Rocznik
Tom
Numer
Strony
171-200
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
• Department of Mathematics, Samara State University, Samara, Russia
autor
• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
autor
• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
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