Hausdorff-Besicovitch dimension of graphs and \(p\)-variation of some Lévy processes (Q880471)

The author looks at several special cases of Lévy processes used in financial modelling, such as Carr-Geman-Madan-Yor, normal inverse Gaussian, generalized hyperbolic, or Meixner processes, defined either by the Lévy measure or by the closed form of the characteristic exponent, and studies the Hausdorff dimension of the graph of these processes. It is suggested that this can be used to find the right model for given data sets. The underlying general result gives the Hausdorff dimension of the graph of a real-valued Lévy process if the upper and lower Blumenthal-Getoor indices agree.