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

Sergey Astashkin, Fedor Sukochev, and Chin Pin Wong. "Disjointification of martingale differences and conditionally independent random variables with some applications." Studia Mathematica 205.2 (2011): 171-200. <http://eudml.org/doc/285640>.

@article{SergeyAstashkin2011,
abstract = {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 xk’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.},
author = {Sergey Astashkin, Fedor Sukochev, Chin Pin Wong},
journal = {Studia Mathematica},
keywords = {disjointification inequality; conditionally independent random variables; Rosenthal inequality; symmetric function spaces},
language = {eng},
number = {2},
pages = {171-200},
title = {Disjointification of martingale differences and conditionally independent random variables with some applications},
url = {http://eudml.org/doc/285640},
volume = {205},
year = {2011},
}

TY - JOUR
AU - Sergey Astashkin
AU - Fedor Sukochev
AU - Chin Pin Wong
TI - Disjointification of martingale differences and conditionally independent random variables with some applications
JO - Studia Mathematica
PY - 2011
VL - 205
IS - 2
SP - 171
EP - 200
AB - 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 xk’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.
LA - eng
KW - disjointification inequality; conditionally independent random variables; Rosenthal inequality; symmetric function spaces
UR - http://eudml.org/doc/285640
ER -