Séminaire de Probabilités XLIV pp 61-74

Part of the Lecture Notes in Mathematics book series (LNM, volume 2046) | Cite as

Some Classes of Proper Integrals and Generalized Ornstein–Uhlenbeck Processes

  • Andreas Basse-O’Connor
  • Svend-Erik Graversen
  • Jan Pedersen
Chapter

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.

Keywords

Stochastic integration Lévy processes Generalized Ornstein–Uhlenbeck processes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas Basse-O’Connor
    • 1
  • Svend-Erik Graversen
    • 2
  • Jan Pedersen
    • 2
  1. 1.Department of MathematicsThe University of TennesseeKnoxvilleUSA
  2. 2.Department of Mathematical SciencesUniversity of AarhusAarhus CDenmark

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