Modelling with given reliability and accuracy in the space $L_p(T)$ of stochastic processes from $Sub_\varphi(\Omega)$ decomposable in series with independent elements

Models that approximate stochastic processes from $Sub_\varphi(\Omega)$ with given reliability and accuracy in $L_p(T)$ for some given $\varphi(t)$ are considered. We also study construction of models of processes which can be decomposed into series with approximate elements. Karhunen-Lo{\`e}ve model is considered as an example of the application of the proposed construction.