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Lévy processes on Hilbert Spaces

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Stochastic Models for Prices Dynamics in Energy and Commodity Markets

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Abstract

We introduce and study Lévy process in Hilbert space. These processes are the basic noise drivers in the forward price dynamics. Explicit constructions based on subordination of Wiener process to define normal inverse Gaussian, stable and variance-gamma Lévy processes with values in Hilbert space are provided.

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Notes

  1. 1.

    the French acronym càdlàg means continuous from the right, limits from the left.

  2. 2.

    By \(\boldsymbol {\theta }\leq \boldsymbol {\theta }_1\) we mean that \(\theta _j\leq \theta _{1,j}\) for all \(j=1,\ldots ,d\).

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Authors and Affiliations

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

    Fred Espen Benth

  2. Institute for Statistics and Mathematics, Vienna University of Economics and Business, Vienna, Austria

    Paul Krühner

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  1. Fred Espen Benth
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  2. Paul Krühner
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Benth, F.E., Krühner, P. (2023). Lévy processes on Hilbert Spaces. In: Stochastic Models for Prices Dynamics in Energy and Commodity Markets. Springer Finance. Springer, Cham. https://doi.org/10.1007/978-3-031-40367-5_2

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