Abstract
We prove an estimate for weighted $p$th moments of the pathwise $r$-variation of a martingale in terms of the $A_{p}$ characteristic of the weight. The novelty of the proof is that we avoid real interpolation techniques.
Citation
Pavel Zorin-Kranich. "Weighted Lépingle inequality." Bernoulli 26 (3) 2311 - 2318, August 2020. https://doi.org/10.3150/20-BEJ1194
Information
Received: 1 August 2019; Published: August 2020
First available in Project Euclid: 27 April 2020
zbMATH: 07193961
MathSciNet: MR4091110
Digital Object Identifier: 10.3150/20-BEJ1194
Keywords:
$p$-variation
,
Burkholder–Davis–Gundy inequality
,
Muckenhoupt $A_{p}$ weight
Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability
