Summary
Necessary and sufficient conditions are obtained for: (i) convergence of row products from a null triangular array of renewal sequences to a particular renewal sequence and (ii) convergence of an infinite product of renewal sequences to a non-trivial limit. These products correspond to intersections of regenerative phenomena of integers. Lévy processes of such regenerative phenomena are constructed.
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Research partially supported by National Science Foundation Grant MCS 78-01168
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Fristedt, B. The central limit problem for, infinite products of, and Lévy processes of renewal sequences. Z. Wahrscheinlichkeitstheorie verw Gebiete 58, 479–507 (1981). https://doi.org/10.1007/BF00534944
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DOI: https://doi.org/10.1007/BF00534944