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1.
Davar Khoshnevisan Yimin Xiao 《Proceedings of the American Mathematical Society》2008,236(7):2597-2607
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.
2.
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.