This paper reviews a class of multifractal models obtained via products of exponential Ornstein–Uhlenbeck processes driven by Lévy motion. Given a self-decomposable distribution, conditions for constructing multifractal scenarios and general formulas for their Renyi functions are provided....

Continuous non-Gaussian stationary processes of the OU-type are becoming increasingly popular given their flexibility in modelling stylized features of financial series such as asymmetry, heavy tails and jumps. The use of non-Gaussian marginal distributions makes likelihood analysis of these...

We provide a simulation procedure for obtaining discretely observed values of Ornstein-Uhlenbeck processes with given (self-decomposable) marginal distribution. The method proposed, based on inversion of the characteristic function, completely circumvent problems encountered when trying to...

This paper presents the first empirical investigation of the Multifractal Model of Asset Returns ("MMAR"). The MMAR, developed in Mandelbrot, Fisher, and Calvet (1997), is an alternative to ARCH-type representations for modelling temporal heterogeneity in financial returns. Typically,...

We provide necessary and sufficient conditions on the characteristics of an infinitely divisible distribution under which its characteristic function φ decays polynomially. Under a mild regularity condition this polynomial decay is equivalent to 1/φ being a Fourier multiplier on Besov spaces.

We congratulate the authors for the interesting paper. The reading has been really pleasant and instructive. We discuss briefly only some of the interesting results given in Devroye and James (Stat Methods Appl 2014) with particular attention to evolution problems. The contribution of the...

For a broad class of Markov processes, we give a new intrinsic limit theorem for local time at a point x0. We suitably normalize the number of dyadic time boxes where the process passes through x0 before t0. We discuss the relation with other normalizations. We apply this result to the theory of...

We study the existence of moments and the tail behaviour of the densities of storage processes. We give sufficient conditions for existence and non-existence of moments using the integrability conditions of submultiplicative functions with respect to Lévy measures. Then, we study the...

In this work, we study the solutions of some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be expressed by means of the transition laws of stable...