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.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Establishes finite-sample MSE bounds separating discretization and fluctuation errors for expected signature estimation under summable block-signature covariance, applicable to fractional Ornstein-Uhlenbeck processes across Hurst regimes.
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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.
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Finite-Sample Bounds for Expected Signature Estimation under Weak Dependence
Establishes finite-sample MSE bounds separating discretization and fluctuation errors for expected signature estimation under summable block-signature covariance, applicable to fractional Ornstein-Uhlenbeck processes across Hurst regimes.