Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Naganuma, Nobuaki
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7223674946