DISTRIBUTION OF THE FINAL EXTENT OF A RUMOR PROCESS

A rumour model due to Maki and Thompson (1973) is slightly modified to incorporate a continuous-time random contact process and varying indi vidual behaviours in front of the rumour. Two important measures of th e final extent of the rumour are provided by the ultimate number of pe ople who have heard the rumour, and the total personal time units duri ng which the rumour is spread. Our purpose in this note is to derive t he exact joint distribution of these two statistics. That will be done by constructing a family of martingales for the rumour process and th en using a particular family of Gontcharoff polynomials.