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


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.

Share and Cite:

A. Kozhevnikov and K. Rybakov, "Analysis of Nonlinear Stochastic Systems with Jumps Generated by Erlang Flow of Events," Open Journal of Applied Sciences, Vol. 3 No. 1, 2013, pp. 1-7. doi: 10.4236/ojapps.2013.31001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] V. S. Pugachev and I. N. Sinitsyn, “Stochastic Systems: Theory and Applications,” World Scientific, New Jersey, 2001.
[2] I. E. Kazakov, V. M. Artem’ev and V. A. Bukhalev, “Analysis of Systems with Random Structure,” Fizmatlit, Moscow, 1993. (In Russian: И. Е. Казаков, В. М. Арте-мьев, В. А. Бухалев, “Анализ систем случайной стру- ктуры,” Физматлит, Москва, 1993.)
[3] F. B. Hanson, “Applied Stochastic Processes and Control for Jump-Diffusions,” SIAM, Philadelphia, 2007.
[4] V. V. Solodovnikov, V. V. Semenov, M. Peschel and D. Nedo, “Design of Control Systems on Digital Computers: Spectral and Interpolational Methods,” Verlag Technik, Berlin; Maschinostrojenije, Moscow, 1979. (In German: W. W. Solodownikow, W. W. Semjonow, M. Peschel and D. Nedo, “Berechnung von Regelsystemen auf Digital rechnern: Anwendung von Spektral und Interpolation smethoden,” Verlag Technik, Berlin, 1979; In Russian: В. В. Солодовников, В. В. Семенов, М. Пешель, Д. Недо, “Расчет систем управления на ЦВМ: спектральный и интерполяционный методы,” Машиностроение, Мо сква, 1979.)
[5] 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.)
[6] A. V. Panteleev and K. A. Rybakov, “Analyzing Nonlinear Stochastic Control Systems in the Class of Generalized Characteristic Functions,” Automation and Remote Control, Vol. 72, No. 2, 2011, pp. 393-404. doi:10.1134/S0005117911020159
[7] F. A. Haight, “Handbook of the Poisson Distribution,” John Wiley & Sons, New York, 1967.
[8] K. A. Rybakov and I. L. Sotskova, “Spectral Method for Analysis of Switching Diffusions,” IEEE Transactions on Automatic Control, Vol. 52, No. 7, 2007, pp. 1320-1325. doi:10.1109/TAC.2007.900841
[9] M. Lindner, “Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method,” Birk- h?user, Basel, 2006.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.