We introduce a family of random measures $M_{H,T} (d t)$, namely log S-fBM, such that, for $H>0$, $M_{H,T}(d t) = e^{\omega_{H,T}(t)} d t$ where $\omega_{H,T}(t)$ is Gaussian process that can be considered as stationary version an $H$-fractional Brownian motion. Moreover, when $H \to 0$, one has \rightarrow {\widetilde M}_{T}(d t)$ (in the weak sense) ${\widetilde celebrated log-normal multifra...

We prove that multifractal functions, characterized by their wavelet representation can be estimated in the white noise model by a Bayesian estimation 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.

The financial crisis has fueled interest in alternatives to traditional asset classes that might be less affected by large market gyrations and, thus, provide for a less volatile development of a portfolio. One attempt at selecting stocks that are less prone to extreme risks, is obeyance of Islamic Sharia rules. In this light, we investigate the statistical properties of the Dow Jones Islamic S...

We describe the main features of wavelet techniques in multifractal analysis, using wavelet bases both as a tool for analysis, and for synthesis. We focus on two promising developments: On the analysis side, we introduce the quantile leader method, which allows to put into light nonconcave multifractal spectra; on the synthesis side, we study some extensions of random wavelet series which allow...

Abstract. Some asymptotic properties of a Brownian motion in multifractal time, also called multifractal random walk, are established. We show the almost sure and L convergence of its structure function. This is an issue directly connected to the scale invariance and multifractal property of the sample paths. We place ourselves in a mixed asymptotic setting where both the observation length and...

The design of appropriate multifractal analysis algorithms, able to correctly characterize the scaling properties of multifractal systems from experimental, discretized data, is a major challenge in the study of such scale invariant systems. In the recent years, a growing interest for the application of the microcanonical formalism has taken place, as it allows a precise localization of the fra...

Physical variables in scale invariant systems often show chaotic, turbulent-like behaviour, what is commonly associated to the existence of a fractal or multifractal underlying structure. The detection of such structure over experimental data requires appropriate methods of analysis and to establish criteria to measure the confidence degree in the estimates. In this paper we will test four diff...

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi(4)-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties that are necessarily found for...

This paper focuses on the differences between monofractal and multifractal network traffic, both in terms of modeling approaches, and in terms of practical impacts on network performance. Empirical traffic traces are used in the parameterization and evaluation of traffic models. Simulation is used to evaluate the performance differences between monofractal and multifractal traffic, both for ind...