A transformation from Hausdorff to Stieltjes moment sequences

Christian Berg Department of Mathematics, University of Copenhagen Antonio J. Durán Departamento de Análisis Matemático, Universidad de Sevilla

TBD mathscidoc:1701.333032

Arkiv for Matematik, 42, (2), 239-257, 2003.4
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$T$[($a$_{$n$})_{$n$=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 to$q$-series.
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  title={A transformation from Hausdorff to Stieltjes moment sequences},
  author={Christian Berg, and Antonio J. Durán},
  booktitle={Arkiv for Matematik},
Christian Berg, and Antonio J. Durán. A transformation from Hausdorff to Stieltjes moment sequences. 2003. Vol. 42. In Arkiv for Matematik. pp.239-257. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203611097192841.
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