We considered a method for the determining of the statistical characteristics of the magnitude, location and first-passage time of Markov random process, with piecewise constant drift and diffusion coefficients. We found the closed analytical expressions for distribution functions of the specified random variables. We also analyzed the asymptotic behavior of probability density and ordinary moments of location of the greatest maximum of Markov random process and showed their coincidence with some known results for the particular cases.
We are considering a problem of the measurement of the dispersion of the random pulse signal with unknown time of arrival against the white noise and the correlated Gaussian interference. By applying a maximum likelihood method, we synthesize quasi-optimal, quasi-likelihood and adaptive estimation algorithms. We also find out the theoretical and experimental dependences for the characteristics of the obtained dispersion estimates that are then used in the study of the efficiency of the introduced algorithms and in the further investigation revea-6936 O.V. Chernoyarov et al. ling the loss in estimation accuracy, due to the absence of the prior information on intensity of operational interferences. We are to show that, with the adaptation in terms of intensity of the correlated interference, it is possible to obtain the dispersion estimate independent from the intensity of white noise, and its characteristics coincide asymptotically with the corresponding characteristics of the dispersion estimate, obtained under the a priori known intensities of interference and white noise.
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