{ Fractional calculus allows to generalize the standard (linear and one dimensional) diiusion equation by replacing the second-order space derivative by a derivative of fractional order. If this is taken as the pseudo-diierential operator introduced by Feller in 1952 the fundamental solution of the resulting diiusion equation is a probability density evolving in time and stable in the sense of ...

Absorption of acoustic wave propagation in a large variety of lossy media is characterized by an empirical power law function of frequency, 0j!j y . It has long been noted that the exponent y ranges from 0 to 2 for diverse media. Recently, the present author [J. Acoust. Soc. Am. 115 (2004) 1424] developed a fractional Laplacian wave equation to accurately model the power law dissipation, which ...

We use a rapidly rotating tank lled with water to study the random walks of tracer particles in two di erent ows: one with coherent structures (vortices and jets), and one without (weakly turbulent). Most random walks, such as those taken by dye molecules di using by Brownian motion, obey the Central Limit Theorem; their motion can be characterized by a di usion constant. The random walks in ou...

1 Abstract Wolfe 1982 and Sato 1991 gave t wo diierent representations of a random variable X 1 with a self-decomposable distribution in terms of processes with independent increments. This paper shows how either of these representations follows easily from the other, and makes these representations more explicit when X 1 is either a rst or last passage time for a Bessel process.

Huet and L evy deened the (orthogonal) strongly sequential term rewriting systems, for which index reduction, i.e., reduction of re-dexes placed at special positions called (strong) indices, is optimal and normalizing. Despite the fact that Huet and L evy give an algorithm to compute indices for the general case, there are many proposals to deene subclasses of strongly sequential rewrite system...

We provide a systematic analysis of the possible asymptotic distributions of one-dimensional continuous-time random walks (CTRWs) by applying the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previous works concerning decoupled memory and L evy walks, we deal also with arbitrary coupled memory and with jump densiti...

The main result of the paper is a constructive proof of the following equivalence: two pure -terms are observationally equivalent in the lazy concurrent -calculus i they have the same L evy-Longo trees. An algorithmwhich allows to build a context discriminating any two pure -terms with di erent L evy-Longo trees is described. It follows that contextual equivalence coincides with behavioural equ...

A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing \stable" L evy processes. This model can be understood as a continuum limit of discrete state-space, two allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitable large space and tim...

The moderate deviations principle is shown for the partial sums processes built on U-empirical measures of Polish space valued random variables and on U-statistics of real valued kernel functions. It is proved that in the non-degenerate case the conditions for the time xed principles suuce for the moderate deviations principle to carry over to the corresponding partial sums processes. Given a u...