We complement the theory of tick-by-tick dynamics of financial markets based on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et al [4], and we point out its consistency withâ€¦ (More)

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walkâ€¦ (More)

In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse theâ€¦ (More)

{ Fractional calculus allows one to generalize the linear (one dimensional) diiusion equation by replacing either the rst time derivative or the second space derivative by a derivative of aâ€¦ (More)

The Mellin transform is usually applied in probability theory to the product of independent random variables. In recent times the machinery of the Mellin transform has been adopted to describe theâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2004

A detailed study is presented for a large class of uncoupled continuous-time random walks. The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusiveâ€¦ (More)

The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW) is presented starting from its representation as an infinite series that pointsâ€¦ (More)

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index Î± (0 < Î± â‰¤ 2), in the symmetric case. We show that byâ€¦ (More)

In recent years considerable interest in fractional calculus has been stimulated by the applications it finds in different areas of applied sciences like physics and engineering, possibly includingâ€¦ (More)

It is our intention to provide via fractional calculus a generalization of the pure and compound Poisson processes, which are known to play a fundamental role in renewal theory, without and withâ€¦ (More)