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Rough path lifts of multifractional Brownian motions
Nobuaki Naganuma
Source 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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