In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.
Wang, Yan & Wang, Lei & Zhao, Yanxiang & Song, Aimin & Ma, Yanping. (2015). A stochastic model for microbial fermentation process under Gaussian white noise environment. Numerical Algebra, Control and Optimization. 5. 381-392.