Anomalies in Multifractal Formalism for Local Time of Brownian Motion

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Abstract

The Renyi function for the logical time measure μ of Brownian motion is found. It is shown that this function, the Legendre transform of the multifractal spectrum of μ and the τ-function derived by the reciprocal measure formalism are not identical. More examples of μ having similar anomalies are discussed.

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