An explicit view of the optimal lagged filtration operator for an L-Markov process

Abstract

An explicit view of the optimal lagged filtration operator for an L-Markov process

Fadeeva L.Yu.

Incoming article date: 16.06.2025

The paper develops an algorithm for constructing an optimal lagged filtration operator for an L-Markov process. The explicit formula of the filtration operator is obtained on the basis of methods for calculating stochastic integrals and the theory of analytical functions of a complex variable using spectral analysis and the theory of L-Markov processes. An interesting example of an optimal lagged filtration operator for an L-Markov process is considered, which can be used for modeling and controlling complex stochastic systems. It is shown that this operator is represented as a linear combination of the values of the received signal and an integral with an exponentially decaying function.

Keywords: random process, L-Markov process, noise, lag filtering, spectral characteristic, filtering operator