Journal article
On the Behavior of the Constant in a Decoupling Inequality for Martingales
Proceedings of the American Mathematical Society, v 121(1), pp 253-258
1994
Abstract
Let (fn) and (gn) be two martingales with respect to the same filtration (Fn) such that their difference sequences (dn) and (en) satisfy P(dn≥ λ∣Fn - 1) = P(en≥ λ∣Fn - 1) for all real λ's and n ≥ 1. It is known that$\|f^\ast\|_p \leq K_p\|g^\ast\|_p,\quad 1 \leq p < \infty,$for some constant Kpdepending only on p. We show that Kp= O(p). This will be obtained via a new version of Rosenthal's inequality which generalizes a result of Pinelis and which may be of independent interest.
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Details
- Title
- On the Behavior of the Constant in a Decoupling Inequality for Martingales
- Creators
- Paweł Hitczenko
- Publication Details
- Proceedings of the American Mathematical Society, v 121(1), pp 253-258
- Publisher
- American Mathematical Society
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Scopus ID
- 2-s2.0-84966231986
- Other Identifier
- 991020531944904721