Abstract
We give necessary and sufficient conditions for existence of proper integrals from 0 to infinity or from minus infinity to 0 of one exponentiated Lévy process with respect to another Lévy process. The results are related to the existence of stationary generalized Ornstein–Uhlenbeck processes. Finally, in the square integrable case the Wold-Karhunen representation is given.
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Basse-O’Connor, A., Graversen, SE., Pedersen, J. (2012). Some Classes of Proper Integrals and Generalized Ornstein–Uhlenbeck Processes. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIV. Lecture Notes in Mathematics(), vol 2046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27461-9_3
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DOI: https://doi.org/10.1007/978-3-642-27461-9_3
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