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arXiv · 2610.32201

Rough path lifts of multifractional Brownian motions

Nobuaki Naganuma
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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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Nobuaki Naganuma. 2026-10-23. Rough path lifts of multifractional Brownian motions. https://arxiv.org/abs/2610.32201

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