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This paper develops a method for estimating the Hurst function of a multifractional Brownian motion, which is an extension of the fractional Brownian motion in the sense that the path regularity can now vary with time. This method is based on a local estimation of the second order moment of a unique discretized ltered path. The eectiveness of our procedure is investigated in a short simulation study.doi:10.3150/bj/1137421637 fatcat:akngrt3dazcmhpizcovcquuigq