Estimating main characteristics of processes with non-regular observations

Abstract

In this paper the amplitude modulated version of a random process is investigated. Two cases have been taken into consideration.
When the irregularities in observations are defined as a Poisson sequence, the estimators of the covariance function and the spectral density have been constructed. When the irregularities in observations are defined as a stationary random process in the wide sense, the estimators of the mean and the covariance function have been constructed. Statistical properties of the estimators have been studied.