Arkiv för Matematik

  • Ark. Mat.
  • Volume 42, Number 2 (2004), 239-257.

A transformation from Hausdorff to Stieltjes moment sequences

Christian Berg and Antonio J. Durán

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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 formula T[(an) ${}_{n=1}^{∞}$ ]n = 1/a1 ... an. 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 to q-series.


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).

Article information

Ark. Mat., Volume 42, Number 2 (2004), 239-257.

Received: 8 April 2003
Revised: 30 May 2003
First available in Project Euclid: 31 January 2017

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2004 © Institut Mittag-Leffler


Berg, Christian; Durán, Antonio J. A transformation from Hausdorff to Stieltjes moment sequences. Ark. Mat. 42 (2004), no. 2, 239--257. doi:10.1007/BF02385478.

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