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Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space

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Computation and Combinatorics in Dynamics, Stochastics and Control (Abelsymposium 2016)

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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.

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Notes

  1. 1.

    The odd labelling of these constants stems from an interpretation of CARMA processes as solutions to higher-order linear stochastic differential equations.

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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.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Oslo, Oslo, Norway

    Fred Espen Benth

  2. Facultat de Matematiques, Universitat de Barcelona, Barcelona, Spain

    André Süss

Authors
  1. Fred Espen Benth
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  2. André Süss
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Corresponding author

Correspondence to Fred Espen Benth .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Elena Celledoni

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Giulia Di Nunno

  3. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Kurusch Ebrahimi-Fard

  4. Department of Mathematics, University of Bergen, Bergen, Norway

    Hans Zanna Munthe-Kaas

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Benth, F.E., Süss, A. (2018). Continuous-Time Autoregressive Moving-Average Processes in Hilbert Space. In: Celledoni, E., Di Nunno, G., Ebrahimi-Fard, K., Munthe-Kaas, H. (eds) Computation and Combinatorics in Dynamics, Stochastics and Control. Abelsymposium 2016. Abel Symposia, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-01593-0_11

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