Bistable behaviour of a jump-diffusion driven by a periodic stable-like additive process

We study a bistable gradient system perturbed by a stable-like additive process with a periodically varying stability index. Among a continuum of intrinsic time scales determined by the values of the stability index we single out the characteristic time scale on which the system exhibits the metastable behaviour, namely it behaves like a time discrete two-state Markov chain.

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