Estimation of accuracy and reliability of models of $\varphi$-sub-Gaussian stochastic processes in $C(T)$ spaces

Abstract

At present, in the theory of stochastic process modeling a problem of assessment of reliability and accuracy of stochastic process model in $C(T)$ space wasn't studied for the case of implicit decomposition of process in the form of a series with independent terms. The goal is to study reliability and accuracy in $C(T)$ of models of processes from $Sub_\varphi(\Omega)$ that cannot be decomposed in a series with independent elements explicitly. Using previous research in the field of modeling of stochastic processes, assumption is considered about possibility of decomposition of a stochastic process in the series with independent elements that can be found using approximations. Impact of approximation error of process decomposition in series with independent elements on reliability and accuracy of modeling of stochastic process in $C(T)$ is studied. Theorems are proved that allow estimation of reliability and accuracy of a model in $C(T)$ of a stochastic process from $Sub_\varphi(\Omega)$ in the case when decomposition of this process in a series with independent elements can be found only with some error, for example, using numerical approximations.