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Numerical Algebra, Control and Optimization (NACO)
 

A stochastic model for microbial fermentation process under Gaussian white noise environment

Pages: 381 - 392, Volume 5, Issue 4, December 2015      doi:10.3934/naco.2015.5.381

 
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Yan Wang - School of Science, Dalian Jiaotong University,Dalian, MO 116028, China (email)
Lei Wang - School of Mathematical Sciences, Dalian University of Technology, Dalian, MO 116023, China (email)
Yanxiang Zhao - Department of Mathematics, The George Washington University,Washington DC 20052, United States (email)
Aimin Song - School of Science, Dalian Jiaotong University,Dalian, MO 116028, China (email)
Yanping Ma - Department of Mathematics, Loyola Marymount University, Los Angeles CA 90045, United States (email)

Abstract: 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.

Keywords:  Gaussian white noise, stochastic model, stochastic differential equation, microbial fermentation process.
Mathematics Subject Classification:  Primary: 60H40, 91B70, 91B74 Secondary: 60H10.

Received: March 2015;      Revised: October 2015;      Available Online: October 2015.

 References