Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 295, Issue 1, Pages 134-143Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2004.03.018
Keywords
infinite divisibility; branching processes; random walk; first passage time; Burmann-Lagrange formula; negative binomial distribution; borel distribution; Lambert's W; complete monotonicity
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A class of infinitely divisible distributions on {0, 1, 2,...} is defined by requiring the (discrete) Levy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions. (C) 2004 Elsevier Inc. All rights reserved.
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