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A. V. Panteleev, K. A. Rybakov and I. L. Sotskova, “Spectral Method of Nonlinear Stochastic Control System Analysis,” Vuzovskaya kniga, Moscow, 2006. (In Russian: А. В. Пантелеев, К. А. Рыбаков, И. Л. Сотс?ко?ва, “Спектральный метод анализа нелинейных стохаст ических систем управления,” Вузовская книга, Моск ва, 2006.)

has been cited by the following article:

• TITLE: Analysis of Nonlinear Stochastic Systems with Jumps Generated by Erlang Flow of Events

  AUTHORS: Alexander S. Kozhevnikov, Konstantin A. Rybakov

  KEYWORDS: Analysis; Erlang Flow of Events; Generalized Fokker-Planck Equations; Random Impulses; Jump-Diffusion Process; Spectral Characteristic; Spectral Method Formalism; Stochastic System

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.3 No.1, March 29, 2013

  ABSTRACT: In this paper we consider the stochastic systems with jumps (random impulses) generated by Erlang flow of events that lead to discontinuities in paths. These systems may be used in various applications such as a control of complex technical systems, financial mathematics, mathematical biology and medicine. We propose to use a spectral method formalism to the probabilistic analysis problem for the stochastic systems with jumps. This method allows to get a solution of the analysis problem in an explicit form.