Abstract
Integral quadratic functionals of the trajectories of a normal Markov process are considered. The property of essential unimodality is introduced as a stronger form of unimodality.
This is a preview of subscription content, log in via an institution to check access.
Literature Cited
A. S. Mazmanishvili, Continuum Integration as a Method for Solving Physical Problems [in Russian], Naukova Dumka, Kiev (1987).
D. Slepyan, "Fluctuations of a random signal power," in: Determination of Parameters of Random Signals [in Russian], Gostekhizdat UkrSSR, Kiev (1962), pp. 123–146.
A. J. F. Siegert, "A system approach to a class of problems in the theory of noise and other random phenomena," Trans. IRE,3, 38–44 (March 1957).
I. I. Gikhman and A. V. Skorokhod, Theory of Stochastic Processes [in Russian], Vol. 1, Nauka, Moscow (1971).
E. Lukacs, Characteristic Functions [Russian translation], Nauka, Moscow (1979).
Yu. P. Virchenko and A. S. Mazmanishvili, "Unimodality of one class of distributions associated with the Ornstein—Uhlenbeck complex process," Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1, 55–57 (1988).
I. I. Ibragimov, "On composition of unimodal distributions," Teor. Veroyatn. Ee Primen.,1, No. 2, 283–288 (1956).
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 174–177, March–April, 1992.
Rights and permissions
About this article
Cite this article
Virchenko, Y.P., Mazmanishvili, A.S. Essential unimodality of distributions of random quadratic functionals. Cybern Syst Anal 28, 312–315 (1992). https://doi.org/10.1007/BF01126220
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01126220