We prove that multifractal functions, characterized by their wavelet representation, can be estimated in the white noise model by a Bayesian method. We give rates of convergence for two different models. Further, we study empirical methods for estimating the hyperparameters of the model, which lead to a fully tractable estimator.
"Wavelet estimation of a multifractal function." Bernoulli 11 (2) 221 - 246, April 2005. https://doi.org/10.3150/bj/1116340292