On-Line and Adaptive Optimum Advertising Control by a Diffusion Approximation

We formulate a diffusion approximation to a stochastic advertising model of the Vidale-Wolfe type. This formulation allows solution of problems of optimum and on-line sales forecasting, parameter identification, and advertising control under uncertainty. For practical solutions, we suggest approximations and use simulation to forecast the probabilistic response of sales to an advertising program. Examples contrasting the stochastic process and the diffusion approximations approaches are included.