Abstract
This work is concerned with a stochastic sine-Gordon equation with a fast oscillation governed by a stochastic reaction–diffusion equation. It is shown that the fast component is ergodic, while the slow component is tight. Furthermore, employing the skill of partitioning time interval and borrowing from the averaging principle, the system is reduced into an effective equation. More precisely, the fast oscillation component is averaged out, and there exists an effective process, converging to the original stochastic sine-Gordon equation.
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