Identification of a multifractional Gaussian process with a piece-wise constant scale function

We propose a Gaussian multifractional process with continuous paths, but with a piecewise constant scale function. We call it Step Fractional Brownian Motion (SFBM). Therefore, we get a model to describe phenomenon with continuous paths and abrupt changes in their nature at some times. First, we build our model and then we propose an estimator of the scale function, by detecting the change times and estimating the values of the scale function between these change times. (C) 1999 Academie des Sciences/Editions scientifiques et medicales Elsevier SAS.