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| Dynamics of a Degenerately Damped Stochastic Lorenz-Stenflo System |
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| KeyWord:Lorenz-Stenflo system, invariant measure, Lyapunov function, noise-induced stabilization |
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| 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. |
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