Exact Solutions of Stochastic Differential Equations: Gompertz, Generalized Logistic and Revised Exponential

Abstract

Exact analytic solutions of some stochastic differential equations are given along with characteristic futures of these models as the Mean and Variance. The procedure is based on the Ito calculus and a brief description is given. Classical stochastic models and also new models are provided along with a related bibliography. Stochastic models included are the Gompertz, Linear models with multiplicative noise term, the Revised Exponential and the Generalized Logistic. Emphasis is given in the presentation of stochastic models with a sigmoid form for the mean value. These models are of particular interest when dealing with the innovation diffusion into a specific population, including the spread of epidemics, diffusion of information and new product adoption.