Spreading dynamics of stochastic Fisher–KPP equations perturbed by mean-reverting processes
Abstract
Abstract In this paper, we investigate how mean-reverting processes affect the asymptotic propagation speed of the Fisher–KPP equation. The considered mean-reverting processes include the Black–Karasinski process, the Ornstein–Uhlenbeck process and the Cox–Ingersoll–Ross process. We introduce averaging principles for stochastic fast and slow systems to illustrate that the impacts are determined by their time-average limits. To demonstrate this, we refine the methods developed by Elworthy, Øksendal et al presented in (1994 Math. Comput. Modelling 20 131–66) and (2001 Nonlinearity 14 639–62), by incorporating ergodicity analyses.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Stochastic processes and statistical mechanics
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 2
- Pages
- 025013–025013
- Publication date
- 26 February 2026
- Language
- EN