Diffusion of information in a random environment

The effects of random environmental fluctuations on the process of diffusion of information in a social group are investigated. The methodology of this investigation is based on a study of “stochastic differential equations with fluctuating parameters,” under the assumption that the time scale of the fluctuations in the various parameters is much shorter than that of the macroscopic variables of the system. This enables us to convert a stochastic differential equation into a Fokker‐Planck equation which in turn can be solved for obtaining an explicit expression for the stationary state of the system. As an illustration, we analyze various cases of Bartholomew's model of diffusion of information in a randomly fluctuating environment and calculate the relevant statistical characteristics of interest. The resulting effects of environmental stochasticity on the process of diffusion of information are compared with the ones arising from the intrinsic stochasticity of the process, the latter depending inevitably on the size of the population group involved.

Notes

On leave of absence from the University of Delhi, Delhi‐110007 India.