Continuous multifractal models with zero values: a continuous β-multifractal model.
Résumé
In this paper we propose for the rst time a multiplicative continuous model for generating multifractal elds with zero values, as a continuous generalization of the intermittent lognormal -model proposed by Over and Gupta (1996). It is built using in nitely multiplicative random variables, the multiplicative analog to in nitely divisible distributions for addition. The model also needs stochastic multiplicative measures and multiplicative stochastic integrals. It possesses as a special case a continuous generalization of the classical discrete -model. Applications are numerous in many elds of applied science, including small-scale rainfall and soil science.