Fractional Laplace motion

In English Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it may also prove useful in modeling financial time series. Its one dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one dimensional distributions are more peaked at the mode than a Gaussian, and their tails are heavier. In this paper, we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.