Year: 2023
Author: Liangke Zhou, Caibin Zeng
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 3 : pp. 471–493
Abstract
It seems that little has been known about the sensitivity of steady states in stochastic systems. This paper proves the conditions for the existence of an invariant measure in a degenerately damped stochastic Lorenz-Stenflo model. Precisely, the solution is proved to be a nice diffusion via the Lie bracket technique and non-trivial Lyapunov functions. The finiteness of the expected positive recurrence time entails the existence problem. On the other hand, a cut-off function is constructed to show the non-existence result through a proof by contradiction. For other interesting cases, the expected recurrence time is shown to be infinite.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2023.471
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 3 : pp. 471–493
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Lorenz-Stenflo system invariant measure Lyapunov function noise-induced stabilization.