Stochastic model of innovation diffusion that takes into account the changes in the total market volume

The article proposes a stochastic mathematical model of the diffusion of consumer innovations, which takes into account changes over time in the total number of potential buyers of an innovative product. A stochastic differential equation is constructed for a random value of the number of consumers of an innovative product. The interaction of random changes in the number of consumers with changes in the total market volume of the product under consideration is investigated. Following the Euler – Maruyama method, an algorithm for the numerical solution of the stochastic differential equation for the diffusion of innovations is constructed. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for a random function of the number of consumers of an innovative product. A variant of the method for calculating the mathematical expectation of a random function of the number of consumers of an innovative product is developed and the corresponding differential equation is obtained. It is shown that the numerical solution of this equation and the average value of the function of the number of consumers calculated for all the implemented implementations of stochastic trajectories give practically the same results. Numerical analysis of the developed model showed that taking into account an external random disturbing factor in the stochastic model leads to significant deviations from the classical deterministic model of smooth market development with innovative goods.