Distribution of absolute maximum of Gaussian Markov’s stationery process
DOI:
https://doi.org/10.3103/S0735272713010068Abstract
The absolute maximum of Gaussian Markov’s stationary process is obtained by means of solution of the Fokker–Planck–Kolmogorov equation with method of variables division. It is shown, known results are special cases of obtained solution. The probability of process location in one of half-plane of its values is specified.
References
YEVGRAFOV, D.V. The reflection method with a change of sign in problems of the quality analysis of signal detection. Radioelectron. Commun. Syst., v.53, n.6, p.333-340, 2010, DOI: 10.3103/S0735272710060075.
TIKHONOV, V.I. AND MIRONOV, M.A., Markov’s Processes. Moscow: Sov. Radio, 1977. 488 p. [in Russian].
BAKUT, V.A., The Signals Detection Theory. Moscow: Radio i Svyaz’, 1084. 439 p. [in Russian].
TRIFONOV, A.P. AND SHINAKOV, YU.S., Mutual Signals Detection and their Parameters Estimation on a Background of Interferences. Moscow: Radio i Svyaz’, 1986 [in Russian].
PICKANDS, J., Uprossing probabilities for stationary Gaussian process. Trans. Amer. Math. Soc., n.III, Nov. 1969.
PITERBARG, V.I., About Pickands’s paper. Probabilities for intersection of stationery Gaussian process. Vesti MGU. Ser. Matematika i Mekhanika, n.5, 1972.
GRADSHTEIN, I.S. AND RYZHIK, I.M., Tables of Integrals, Sums, Series and Products. Moscow: Nauka, 1971 [in Russian].
MORSE, F.M. AND FESHBACH, H., Methods of Theoretical Physics. Vol. 1. New York: McGraw-Hill, 1953.
YANKE, E.; EMDE, F.; LESH, F., Special Functions. Formulas, Graphs, Tables. Moscow: Nauka, 1968. 344 p. [in Russian].
PRUDNIKOV, A.P.; BRYCHKOV, YU.A.; MARICHEV, O.I., Integrals and Series, Special Functions. Moscow: Nauka, 1983. 752 p. [in Russian].
PRUDNIKOV, A.P.; BRYCHKOV, YU.A.; MARICHEV, O.I., Integrals and Series. Moscow: Nauka, 1981. 797 p. [in Russain].