We consider stochastic processes $Y(t)$ which can be represented as $Y(t)=(X(t))^s, s \in \mathbb{N},$ where $X(t)$ is a stationary strictly sub-Gaussian process and build a wavelet-based model that simulates $Y(t)$ with given accuracy and reliability in $L_p([0,T])$. A model for simulation with given accuracy and reliability in $L_p([0,T])$ is also built for processes $Z(t)$ which can be represented as $Z(t)=X_1(t) X_2(t)$, where $X_1(t)$ and $X_2(t)$ are independent stationary strictly sub-Gaussian processes.