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Rough path lifts of multifractional Brownian motions
Abstract
We show that multifractional Brownian motions (mBms) can be lifted to geometric rough paths. One of the main ingredients in the proof is a decomposition of mBms via the Lemarié-Meyer orthogonal wavelet basis, which is introduced in the context of multiresolution analysis. As a consequence, we are able to construct solutions to rough differential equations driven by mBms.
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BibTeX
@misc{naganuma2026rough,
title = {{Rough path lifts of multifractional Brownian motions}},
author = {Nobuaki Naganuma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32201},
eprint = {2610.32201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32201},
}
RIS
TY - UNPB
TI - Rough path lifts of multifractional Brownian motions
AU - Nobuaki Naganuma
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32201
UR - https://arxiv.org/abs/2610.32201
AB - We show that multifractional Brownian motions (mBms) can be lifted to geometric rough paths. One of the main ingredients in the proof is a decomposition of mBms via the Lemarié-Meyer orthogonal wavelet basis, which is introduced in the context of multiresolution analysis. As a consequence, we are able to construct solutions to rough differential equations driven by mBms.
ER -