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Journal of the London Mathematical Society 1989 s2-40(3):563-576; doi:10.1112/jlms/s2-40.3.563
© 1989 by London Mathematical Society
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© Oxford University Press

Perturbation and Rearrangement Aspects of Renewal and Harmonic Renewal Sequences

Rudolf Grübel and Susan M. Pitts

Department of Mathematics and Informatics, Delft University of Technology Julianalaan 132, 2628 BL Delft, The Netherlands
Department of Mathematics, Imperial College of Science and Technology London SW7 2BZ

Two convolution series arising naturally in various stochastic models are the renewal and the harmonic renewal measure,


Formula
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These can be regarded as sequences if the underlying probability distribution p is concentrated on the integers. We investigate the behaviour of these series under infinitesimal perturbations of p and also obtain alternative series representations with better convergence properties.


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