Large deviation principle of occupation measure for stochastic real Ginzburg-Landau equation driven by $α$-stable noises

We establish a large deviation principle for the occupation measure of the stochastic real Ginzburg-Landau equation driven by $α$-stable noises. The proof is based on a hyper-exponential recurrence criterion. Our result indicates a phenomenon that strong dissipation beats heavy tailed noises to produce a large deviation, it seems to us that this phenomenon has not been reported in the known literatures.

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