Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Le docteur Petrus : notions d'hygiène (2e édition) / par A.-Daniel Lévy,...

Collection : Bibliothèque des écoles et des familles

Une Aventure d'éditeurs au XIXe siècle : Michel et Calmann Lévy : [catalogue de l'exposition, 25 avril-24 mai 1986, Paris], Bibliothèque nationale

[Exposition. Paris, Bibliothèque nationale. 1986]

Anticipating linear stochastic differential equations driven by a Lévy process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformations on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].