Normal deviation for a special class of fast slow system with multiplicative noise

In this paper, we investigate normal deviation principles for a specific category of a fast slow system driven by multiplicative noise. By establishing an equivalent transformation framework, we decouple the original coupled system into a fast slow system. Through employing the martingale approach, we derive explicit normal deviation for the multi-scale system. Furthermore, comprehensive numerical simulations are conducted to validate the theoretical findings and demonstrate the practical implications of our results.