Lévy mixing related to distributed order calculus, subordinators and slow diffusions

Lévy Mixing

This paper studies Lévy mixing of multivariate infinitely divisible distributions μ, where the parametrisation is in the form of a rescaling of the Lévy measure and of the cumulant transform of μ by a matrix mapping. Particular examples appear in the study of multivariate operator self-decomposable distributions and the construction of multivariate superpositions of Ornstein-Uhlenbeck processes...

Distributed-order fractional diffusions on bounded domains

Slow Lévy flights.

Among Markovian processes, the hallmark of Lévy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that Lévy laws, as well as Gaussian distributions, can also be the limit distributions of processes with long-range memory that exhibit very slow diffusion, logarithmic in time. These processes are path dependent and anomalous motion emerges from frequent relocations to alre...

From -calculus to Higher-order -calculus | and Back

We compare the rst-order and the higher-order paradigms for the representation of mobility in process algebras. The prototypical calculus in the rst-order paradigm is the-calculus. By generalising its sort mechanism we derive an !-order extension, called Higher-Order-calculus (HO). We give examples of its use, including the encoding of-calculus. Surprisingly, we show that such an extension does...

On Lévy processes, Malliavin calculus and market models with jumps

Recent work by Nualart and Schoutens (2000), where a kind of chaotic property for Lévy processes has been proved, has enabled us to develop a Malliavin calculus for Lévy processes. For simple Lévy processes some useful formulas for computing Malliavin derivatives are deduced. Applications for option hedging in a jump–diffusion model are given.