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The roughness exponent and its model-free estimation

Xiyue Han and Alexander Schied

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Abstract: Motivated by pathwise stochastic calculus, we say that a continuous real-valued function $x$ admits the roughness exponent $R$ if the $p^{\text{th}}$ variation of $x$ converges to zero if $p>1/R$ and to infinity if $p

Date: 2021-11, Revised 2024-06
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