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

TL;DR

This paper develops models for stochastic processes within $Sub_{ ext{phi}}( ext{Omega})$ that achieve specified reliability and accuracy in $L_p(T)$, including series decompositions and applications like the Karhunen-Loève model.

Contribution

It introduces a method to construct models of stochastic processes with prescribed accuracy and reliability, and explores series decompositions including the Karhunen-Loève model as an example.

Findings

Models with specified reliability and accuracy are constructed.

Series decomposition methods for stochastic processes are developed.

Application to the Karhunen-Loève model demonstrates the approach.

Abstract

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.