MPS-RR 1998-1
April 1998

Stationary and selfsimilar processes driven by Lévy processes

Ole E. Barndorff-Nielsen

Victor Pérez-Abreu

Abstract

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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