MPS-RR 1999-2
January 1999

Superposition of Ornstein-Uhlenbeck Type Processes

Ole E. Barndorff-Nielsen

Abstract

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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