Invariant measure of a degenerately damped stochastic Lorenz-Stenflo
AbstractLittle seems to be known about the sensitivity of steady states for
stochastic systems. This paper discusses the problem of whether there is
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 via proof by contradiction. For other interesting
cases, the expected recurrence time is shown to be infinite.