Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-1

April 1998

Using bivariate Lévy processes, stationary and selfsimilar processes, with prescribed one-dimensional marginal laws of type G, are constructed. In the case of square integrability, the arbitrary spectral distribution of the stationary process can be chosen so that the corresponding selfsimilar process has second order stationary increments. The spectral distribution in question, which yields fractional Brownian motion when the driving Lévy process is the bivariate Brownian motion, is shown to possess a density, and an explicit expression for the density is derived.

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