Sato, Ken-iti; Steutel, Fred W. Note on the continuation of infinitely divisible distributions and canonical measures. (English) Zbl 0932.60016 Statistics 31, No. 4, 347-357 (1998). Summary: We consider the question, to what extent an infinitely divisible distribution function on \(\mathbb{R}_+\) is determined by its values on an interval starting at zero, or by the values of its canonical measure on such an interval. These questions are considered in the book by H.-J. Rossberg, B. Jesiak and G. Siegel [“Analytic methods of probability theory” (1985; Zbl 0583.60013)]. Our results extend parts of their work. These results are applied to the continuation of constant multiples of infinitely divisible distribution functions and to the distribution of subordinators. Cited in 1 Document MSC: 60E07 Infinitely divisible distributions; stable distributions Keywords:infinitely divisible distribution function; distribution of subordinators Citations:Zbl 0583.60013 PDFBibTeX XMLCite \textit{K.-i. Sato} and \textit{F. W. Steutel}, Statistics 31, No. 4, 347--357 (1998; Zbl 0932.60016) Full Text: DOI References: [1] Chung K. L., A Course in Probability Theory, 2. ed. (1974) · Zbl 0345.60003 [2] Doss R., Proc. Amer. Math. Soc 104 pp 181– (1988) [3] Feller W., An introduction to probability theory and its application 2, 2. ed. (1971) · Zbl 0219.60003 [4] van Harn K., Math. Centre Tracts 103 (1978) [5] Hartman P., Amer. J. Math. 64 pp 273– (1942) · Zbl 0063.01951 · doi:10.2307/2371683 [6] Rossberg H.-J., Analytic Methods of Probability Theory (1985) · Zbl 0582.60024 [7] Sato K., Z. Wahrsch. verw. Geb. 43 pp 273– (1978) · Zbl 0395.60019 · doi:10.1007/BF00534763 [8] Steutel F. W., Centre Tracts 33 (1970) [9] Vervaat, W. 1972. ”Success epochs in Bernoulli trials, Math.”. Vol. 42, Amsterdam: Math. Centre. · Zbl 0267.60003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.