Stochastic models for fractal processes

This paper considers the situation where a stochastic process may display both long-range dependence (LRD) and intermittency. The existence of such a process is established in Anh et al. (1999). Existing works have commonly paid attention either to LRD or intermittency quite separately. This paper offers a convenient framework to study both effects simultaneously. A method is given to estimate and separate the two effects. The wavelet theory plays an essential role in this procedure. Numerical experiments on fractional Brownian motion and multiplicative cascade processes confirm the power of the method.