JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 205 / 2011

Studia Mathematica 205 (2011), 171-200 MSC: Primary 46B09; Secondary 46E30. DOI: 10.4064/sm205-2-3

#### Streszczenie

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 $L_2$ 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.

#### Autorzy

• Sergey AstashkinDepartment of Mathematics
Samara State University
Samara, Russia
e-mail
• Fedor SukochevSchool of Mathematics and Statistics
University of New South Wales
Sydney, NSW 2052, Australia
e-mail
• Chin Pin WongSchool of Mathematics and Statistics
University of New South Wales
Sydney, NSW 2052, Australia

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek