Asymptotic behaviour of the norm of input-output operators corresponding to singularly perturbed systems with multiplicative white noise

We study the problem of asymptotic property of the norm of input-output operators related to a class of singularly perturbed stochastic linear systems. The system is under perturbation of multiplicative white noise. By using reduction order and boundary layer techniques, it is shown that the norm of the operator of the perturbed system is less than a given number γ when the small perturbation ε tends to zero, if both the related norms of the reduced subsystem and the boundary layer subsystem are less than