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A transformation from Hausdorff to Stieltjes moment sequences

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Arkiv för Matematik

Abstract

We introduce a non-linear injective transformation τ from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formulaT[(a n ) ∞ n=1 ] n = 1/a 1 ...a n . Special cases of this transformation have appeared in various papers on exponential functionals of Lévy processes, partly motivated by mathematical finance. We give several examples of moment sequences arising from the transformation and provide the corresponding measures, some of which are related toq-series.

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Authors and Affiliations

  1. Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark

    Christian Berg

  2. Departamento de Análisis Matemático, Universidad de Sevilla, Apartado 1160, ES-41080, Sevilla, Spain

    Antonio J. Durán

Authors
  1. Christian Berg
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  2. Antonio J. Durán
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Additional information

This work was done while the first author was visiting University of Sevilla supported by the Secretaría de Estado de Educación y Universidades, Ministerio de Ciencia, Cultura y Deporte de España, SAB2000-0142. The work of the second author has been supported by DGES ref. BFM-2000-206-C04-02 and FQM 262 (Junta de Andalucía).

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Berg, C., Durán, A.J. A transformation from Hausdorff to Stieltjes moment sequences. Ark. Mat. 42, 239–257 (2004). https://doi.org/10.1007/BF02385478

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  • DOI: https://doi.org/10.1007/BF02385478

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