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

• Autorzy: Sergey Astashkin , Fedor Sukochev , Chin Pin Wong
• 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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 205
• Numer: 2
• Strony: 171-200

Daty

wydano

2011

Twórcy

autor

Sergey Astashkin

• Department of Mathematics, Samara State University, Samara, Russia

autor

Fedor Sukochev

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

autor

Chin Pin Wong

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

Identyfikatory

DOI

10.4064/sm205-2-3