Explicit formulas for the spectral characteristic and optimal linear filtration operator with a forecast for stochastic L–Markov processes are obtained using methods of spectral analysis of random processes, the theory of functions of a complex variable, and using stochastic differential-difference equations. An interesting example of an optimal filtration operator with a forecast for an L-Markov process with a quasi-rational spectral density generalizing the rational one is constructed for technical applications. It is shown that the forecast filtering operator is the sum of a linear combination of the values of the received signal at some time points and the integral of an exponentially decaying weight function.

Keywords: random process, L-Markov process, prediction filtering, spectral characteristic, filtration operator