scholarly journals Stability of Stochastic Logistic Model with Ornstein-Uhlenbeck Process for Cell Growth of Microorganism in Fermentation Process

2019 ◽  
Vol 10 (08) ◽  
pp. 659-675 ◽  
Author(s):  
Tawfiqullah Ayoubi
Keyword(s):  
Cell Growth ◽  
Logistic Model ◽  
Fermentation Process ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Stochastic Logistic Model

scholarly journals A Note on Stability of Stochastic Logistic Model by Incorporating the Ornstein-Uhlenbeck Process

2020 ◽  
Vol 12 (2) ◽  
pp. 52
Author(s):  
Tawfiqullah Ayoubi ◽  
Abdul Munir Khirzada
Keyword(s):  
Lyapunov Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Logistic Model ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Stochastic Logistic Model

In this research, we first prove that the stochastic logistic model (10) has a positive global solution. Subsequently, we introduce the sufficient conditions for the stochastically stability of the general form of stochastic differential equations (SDEs) in terms of equation (1), for zero solution by using the Lyapunov function. This result is verified via several examples in Appendix A. Besides; we prove that the stochastic logistic model, by incorporating the Ornstein-Uhlenbeck process is stable in zero solution. Furthermore, the simulated results are displayed via the 4-stage stochastic Runge-Kutta (SRK4) numerical method.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

scholarly journals Using the Ornstein–Uhlenbeck process to model the evolution of interacting populations

2017 ◽  
Vol 429 ◽  
pp. 35-45 ◽  
Author(s):  
Krzysztof Bartoszek ◽  
Sylvain Glémin ◽  
Ingemar Kaj ◽  
Martin Lascoux
Keyword(s):  
Uhlenbeck Process ◽  
Interacting Populations ◽  
Ornstein Uhlenbeck Process

On the reflected Ornstein–Uhlenbeck process with catastrophes

2012 ◽  
Vol 218 (23) ◽  
pp. 11570-11582 ◽  
Author(s):  
V. Giorno ◽  
A.G. Nobile ◽  
R. di Cesare
Keyword(s):  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process
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