Spectral representations of quasi-infinitely divisible processes.

This work is divided in three parts. First, we introduce quasi-infinitely divisible (QID) random measures and formulate spectral representations. Second, we introduce QID stochastic integrals and present integrability conditions, continuity properties and spectral representations. Finally, we introduce QID processes, i.e. stochastic processes with QID finite dimensional distributions. For example, a process X is QID if there exist two ID processes Y and Z such that X + Y = d Z with Y independent of X. The class of QID processes is strictly larger than the class of ID processes. We provide spectral representations and Lévy–Khintchine formulations for potentially all QID processes. Many examples are presented. [ABSTRACT FROM AUTHOR]