Continuous time diffusion models with random duration of interest

This paper proposes a continuous time version of a diffusion model introduced by Gray and von Broembsen (1974). The new formulation allows a deeper analysis of the stochastic aspects, of the diffusion process and, in particular, of the threshold effect which occurs in the absence of an outside transmitting source. Attention is drawn to important similarities and differences between the stochastic and the deterministic versions of the model. Simple approximations for the distribution of the ultimate number of hearers are given as well as the exact distribution. Some generalizations are suggested and it is shown that their analysis in deterministic terms is relatively easy.

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