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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-2
January 1999

Superposition of Ornstein-Uhlenbeck Type Processes


Ole E. Barndorff-Nielsen


A class of superpositionsof Ornstein-Uhlenbeck type processes is constructed, in terms of integrals with respect to independently scattered random measures. Under specified conditions the resulting processes exhibit long range dependence. By integration the superpositions yield cumulative processes with stationary increments, and integration with respect to processes of the latter type is defined. A limiting procedure results in processes that, in the case of square integrability, are second order selfsimilar with stationary increments. Certain other of the limiting processes are stable and selfsimilar with stationary increments.

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This paper has now been published in Theory Prob. Its Appl. 45 (2001)