STOCHASTIC MODELS FOR SPREAD OF MOTIVATING INFORMATION.

The paper considers spread of information which motivates the hearer to perform some specified action. The time to completion of an action is assumed to be a random variable and the main focus is on the number of completed actions by time, t, X(t). Some models, which reflect different degree of centralization in the spread process, are analyzed and the distribution of X(t), as well as that of some other stochastic processes of interest, are obtained. The relevance to propagation of epidemics is pointed out. All models are solved by employing two interrelated concepts, the order statistics property of stochastic processes and the binomial closure property of collections of distributions.