Superposition of Ornstein–Uhlenbeck type processes

A class of superpositions of 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 self-similar with stationary increments. Other resulting limiting processes are stable and self-similar with stationary increments.