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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the behavior of the constant in a decoupling inequality for martingales
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by Paweł Hitczenko PDF
Proc. Amer. Math. Soc. 121 (1994), 253-258 Request permission


Let $({f_n})$ and $({g_n})$ be two martingales with respect to the same filtration $({\mathcal {F}_n})$ such that their difference sequences $({d_n})$ and $({e_n})$ satisfy \[ P({d_n} \geq \lambda |{\mathcal {F}_{n - 1}}) = P({e_n} \geq \lambda |{\mathcal {F}_{n - 1}})\] for all real $\lambda$’s and $n \geq 1$. It is known that \[ {\left \| {{f^ \ast }} \right \|_p} \leq {K_p}{\left \| {{g^ \ast }} \right \|_p},\quad 1 \leq p < \infty ,\] for some constant ${K_p}$ depending only on p. We show that ${K_p} = O(p)$. 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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 253-258
  • MSC: Primary 60G42
  • DOI:
  • MathSciNet review: 1176481