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We prove a functional non-central limit theorem for jump-diffusions withperiodic coefficients driven by strictly stable Levy-processes with stabilityindex bigger than one. The limit process turns out to be a strictly stable Levyprocess with an averaged jump-measure. Unlike in the situation where thediffusion is driven by Brownian motion, there is no drift related enhancementof diffusivity.Comment: Accepted to Journal of Theoretical Probabilit

A Functional Non-Central Limit Theorem for Jump-Diffusions with Periodic Coefficients Driven by Stable Lévy-Noise