Abstract
Background. 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 inexplicit decomposition of process in the form of a series with independent terms.Objective. The goal is to study reliability and accuracy in C(T) of models of processes from Subφ(Ω) that cannot be decomposed in a series with independent elements explicitly.Methods. 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.Results. 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.Conclusions. Theorems are proved that allow estimation of reliability and accuracy of a model in C(T) of a stochastic process from Subφ(Ω) 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.
Highlights
In the theory of stochastic processes, modeling of stochastic processes is a vital part
Much attention has been paid to the models of stochastic processes from Sub ( ) spaces, in [1, 2]
We consider models of stochastic processes in C (T ) space when decomposition elements ak (t ) cannot be found explicitly and prove theorems that allow modeling of such stochastic process taking into account errors of approximations of ak (t )
Summary
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 inexplicit 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 ( ) 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 ( ) 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
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