J. Nonl. Mod. Anal., 5 (2023), pp. 471-493.
Published online: 2023-08
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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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.471}, url = {http://global-sci.org/intro/article_detail/jnma/21947.html} }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.