Abstract
This work is concerned with the invariant behavior of a stochastic atmosphere-ocean model with the degenerate noise, which describes the climate and geophysical phenomena. Through introducing a transform to deal with the complicated boundary conditions, first, the existence of the invariant measure is established. Since the degenerate noise only drives the latitudinal atmosphere surface temperature, it then proposes to combine the strong Feller property with the asymptotically strong Feller and the irreducibility to verify the uniqueness of the invariant measure. It further implies the ergodicity of the system.
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