PreprintCC BY 4.0arXiv
A Quantitative Characterization of the Mokobodzki Condition
Abstract
We establish a quantitative characterization of the Mokobodzki condition for two adapted càdlàg barriers on an arbitrary filtered probability space. For every p≥1, we introduce a mean co-variation functional Varp(L,U), which for p=1 and L=U reduces to Rao's mean variation, and show that it is quantitatively equivalent to the minimal underline Hp-norm among all semimartingales lying between the barriers. The result covers both the case p>1 and the endpoint p=1, where the natural scale is based on Doob's class (D).
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BibTeX
@misc{klimsiak2026quantitative,
title = {{A Quantitative Characterization of the Mokobodzki Condition}},
author = {Tomasz Klimsiak and Maurycy Rzymowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16259},
eprint = {2609.16259},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16259},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Quantitative Characterization of the Mokobodzki Condition
AU - Tomasz Klimsiak
AU - Maurycy Rzymowski
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16259
UR - https://arxiv.org/abs/2609.16259
AB - We establish a quantitative characterization of the Mokobodzki condition for two adapted càdlàg barriers on an arbitrary filtered probability space. For every p≥1, we introduce a mean co-variation functional Var_p(L,U), which for p=1 and L=U reduces to Rao's mean variation, and show that it is quantitatively equivalent to the minimal underline H^p-norm among all semimartingales lying between the barriers. The result covers both the case p>1 and the endpoint p=1, where the natural scale is based on Doob's class (D).
ER -