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From Probability Measures to Each Lévy Triplet and Back

In: The Legacy of Kurt Schütte

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  • Horst Osswald

    (Mathematische Institut, LMU)

Abstract

It will be shown that all finite-dimensional Levy processes are completely determined by Borel probability measures on a fixed finite-dimensional Euclidian space in a certain sense. Each Levy process is infinitely close to a fixed multilinear process, living on that space, depending only on the dimension. Levy processes can be identified, if they satisfy the same Levy triplet (Levy-Khintchine formula). The components of this triplet appear in the Fourier transformation of the current probability measure. Lindstroms work “Hyperfinite Levy processes, Stochastics 76 (6) (2004)” is used to show that each Levy triplet is satisfied by an appropriate probability measure on the fixed Euclidian space.

Suggested Citation

  • Horst Osswald, 2020. "From Probability Measures to Each Lévy Triplet and Back," Springer Books, in: Reinhard Kahle & Michael Rathjen (ed.), The Legacy of Kurt Schütte, chapter 0, pages 353-376, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-49424-7_18
    DOI: 10.1007/978-3-030-49424-7_18
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