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Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space

  • Fred Espen BenthEmail author
  • André Süss
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)

Abstract

We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Lévy processes in Hilbert space. We provide the basic definitions, show relevant properties of these processes and establish the equivalents of CARMA processes on the real line. Finally, CARMA processes in Hilbert space are linked to the stochastic wave equation and functional autoregressive processes.

Notes

Acknowledgements

Financial support from the project FINEWSTOCH, funded by the Norwegian Research Council, is gratefully acknowledged. Two anonymous referees are thanked for their positive and constructive critics.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Facultat de MatematiquesUniversitat de BarcelonaBarcelonaSpain

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