Packing dimension of the range of a Lévy process

Let denote a Lévy process in with exponent . Taylor (1986) proved that the packing dimension of the range is given by the index

We provide an alternative formulation of in terms of the Lévy exponent . Our formulation, as well as methods, are Fourier-analytic, and rely on the properties of the Cauchy transform. We show, through examples, some applications of our formula.

     

A combinatorial method for calculating the moments of Lévy area

We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product.