Environmental variability and mean-reverting processes. (English) Zbl 1347.60066
Summary: Environmental variability is often incorporated in a mathematical model by modifying the parameters in the model. In the present investigation, two common methods to incorporate the effects of environmental variability in stochastic differential equation models are studied. The first approach hypothesizes that the parameter satisfies a mean-reverting stochastic process. The second approach hypothesizes that the parameter is a linear function of Gaussian white noise. The two approaches are discussed and compared analytically and computationally. Properties of several mean-reverting processes are compared with respect to nonnegativity and their asymptotic stationary behavior. The effects of different environmental variability assumptions on population size and persistence time for simple population models are studied and compared. Furthermore, environmental data are examined for a gold mining stock. It is concluded that mean-reverting processes possess several advantages over linear functions of white noise in modifying parameters for environmental variability.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 92D25 | Population dynamics (general) |
| 34F05 | Ordinary differential equations and systems with randomness |
| 92B05 | General biology and biomathematics |
Keywords:
stochastic differential equations; mean-reverting process; environmental variability; white noise; population dynamicsReferences:
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