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Zbl 0796.60098
Lefevre, Claude; Picard, Philippe
Distribution of the final extent of a rumour process. (English)
[J] J. Appl. Probab. 31, No.1, 244-249 (1994). ISSN 0021-9002

Summary: A rumour model due to {\it D. P. Maki} and {\it M. Thompson} [Mathematical models and applications (Prentice-Hall, 1973)] is slightly modified to incorporate a continuous-time random contact process and varying individual behaviours in front of the rumour. Two important measures of the final extent of the rumour are provided by the ultimate number of people who have heard the rumour, and the total personal time units during which the rumour is spread. Our purpose is to derive the exact joint distribution of these two statistics. That will be done by constructing a family of martingales for the rumour process and then using a particular family of Gontcharoff polynomials.

MSC 2000:: *60K30 Appl. of queueing theory
60J05 Markov processes with discrete parameter

Keywords: rumour model; Gontcharoff polynomials

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