Modeling of stochastic processes in $L_p(T)$ using orthogonal polynomials

Abstract

In this paper, models that approximate stochastic processes from the space $Su{b}_{\ddot{I}}†(\hat{I}\text{c◯})$ with given reliability and accuracy in $L_p(T)$ are considered for some specific functions $\ddot{I}†(t)$. For processes that are decomposited in series using orthonormal bases, such models are constructed in the case where elements of such decomposition cannot be found explicitly.