Stochastic Dominance for Ito Integral

Consider the stochastic integral $$$$\int_0^t f(s) \mathrm{d}W_s$$$$ for a not necessarily deterministic function $$f$$. Can I bound this random variable in second order stochastic dominance $$\leq_\text{(2)}$$ by an appropriately scaled normal distributed random variable?

Here random variables $$X,Y$$ satisfy $$$$X \leq_\text{(2)} Y$$$$ if and only if for all $$q \in \mathbb{R}$$ $$$$\int_{-\infty}^q F_X(x) \mathrm{d}x \geq \int_{-\infty}^q F_Y(y) \mathrm{d}y$$$$ holds. For simplicity one might assume that $$f$$ is bounded.