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

作者：Astashkin Sergey^*; Sukochev Fedor; Wong Chin Pin

来源：Studia Mathematica, 2011, 205(2): 171-200.

DOI：10.4064/sm205-2-3

• disjointification inequality
• conditionally independent random variables
• Rosenthal inequality
• symmetric function spaces

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 Pena and Hitczenko to the setting of symmetric spaces. Moreover, using these results simplifies the proofs of some modular inequalities.

• 出版日期2011