Modelling with given reliability and accuracy in the space \(L_p(T)\) of stochastic processes from \(\mathrm{Sub}_{\phi}(\Omega)\) decomposable in series with independent elements (Q2850846)

Models that approximate stochastic processes from \(\mathrm{Sub}_{\phi}(\Omega)\) with given reliability and accuracy in the space \(L_p(T)\) for some given \(\phi(t)\) are investigated. The construction of models of the processes which can be decomposed into series \(X(t)=\sum_{k=1}^{\infty}\xi_k a_k(t)\), with independent elements \(\xi_k\), \(\xi_k\in \mathrm{Sub}_{\phi}(\Omega)\), is presented in the form \(X_N(t)=\sum_{k=1}^{N}\xi_k\hat{ a}_k(t)\), where \(\hat{ a}_k(t)\), \(k=1,\dots,N\), approximate \({ a}_k(t)\) with a given accuracy. The Karhunen-Loéve model is considered as an example of application for the proposed construction.