A first-order stationary Markov class a transition density

Abstract

A stationary first-order Markov transition density is constructed from the truncated version of the first- and the second-order probability densities of the Class A noise model, where the random variables described by the multivariate density are correlated. It is analytically shown that the transition function is non-negative and is also a proper density. Moreover, verification that it satisfies the Chapman-Kolmogorov equation is done numerically by obtaining a polynomial approximation for the relationship between two values of the correlation coefficient, one obtained for two successive samples, while the other for two samples with time distance equal to two sampling intervals apart. In general, it is found that the correlation coefficient cannot have a closed form approximation. However, for a set of parameter values of Class A noise, which are typical, it is shown that the correlation coefficient has a simple exponential form. This latter form is often met in signal detection problems with dependent noise sampling.