No local homogeneous rough path lift exists for γ-Hölder paths with γ≤1/2; for fBM with H>1/4 all local square-integrable lifts are stochastic translations of the canonical lift, with only the canonical satisfying extra invariances except at H=1/3.
\ Chevyrev, I
2 Pith papers cite this work, alongside 12 external citations. Polarity classification is still indexing.
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Rough-path market models satisfying no-controlled-free-lunch reduce admissible drivers to Itô lifts of Brownian motion (up to time change) once signature-type strategies are allowed.
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Locality of rough path lifts
No local homogeneous rough path lift exists for γ-Hölder paths with γ≤1/2; for fBM with H>1/4 all local square-integrable lifts are stochastic translations of the canonical lift, with only the canonical satisfying extra invariances except at H=1/3.