Email this article 
Disorder indicator for nonstationary stochastic processes
- Authors: Kislitsyn А.A.1, Kozlova A.B.2, Korsakova M.B.2, Orlov Y.N.1
-
Affiliations:
- Institute for Applied Mathematics of the Russian Academy of Sciences
- N.N. Burdenko National Scientific and Practical Center for Neurosurgery of the Ministry of Healthcare of the Russian Federation
- Issue: Vol 484, No 4 (2019)
- Pages: 393-396
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12542
- DOI: https://doi.org/10.31857/S0869-56524844393-396
- ID: 12542
Cite item
Full Text
Abstract
The properties of a statistic called a self-consistent stationarity level of nonstationary time series are examined in this work. It is shown that a change in this statistic can be treated as a disorder in the nonstationarity properties of the series. The significance level of decision making is estimated, characteristic periods in a non-stationary stochastic process are detected, and an optimal sample size for constructing indicators in stochastic control problems is determined. A disorder indicator for electroencephalogram data from epilepsy patients is studied as a practical application.
About the authors
А. A. Kislitsyn
Institute for Applied Mathematics of the Russian Academy of Sciences
Author for correspondence.
Email: alexey.kislitsyn@gmail.com
Russian Federation, 4, Miusskaya square, Moscow, 125047
A. B. Kozlova
N.N. Burdenko National Scientific and Practical Center for Neurosurgery of the Ministry of Healthcare of the Russian Federation
Email: alexey.kislitsyn@gmail.com
Russian Federation, 16, 4-ya Tverskaya-Yamskaya street, Moscow, 125047
M. B. Korsakova
N.N. Burdenko National Scientific and Practical Center for Neurosurgery of the Ministry of Healthcare of the Russian Federation
Email: alexey.kislitsyn@gmail.com
Russian Federation, 16, 4-ya Tverskaya-Yamskaya street, Moscow, 125047
Yu. N. Orlov
Institute for Applied Mathematics of the Russian Academy of Sciences
Email: alexey.kislitsyn@gmail.com
Russian Federation, 4, Miusskaya square, Moscow, 125047
References
- Королюк В.С., Портенко Н.И., Скороход А.В., Турбин А.Ф. Справочник по теории вероятностей и математической статистике. М.: Наука, 1985. 640 с.
- Кобзарь А.И. Прикладная математическая статистика. М.: Физматлит, 2006. 816 с.
- Орлов Ю.Н. Кинетические методы исследования нестационарных временных рядов. М.: МФТИ, 2014. 276 с.
- Нейрофизиологические исследования в клинике / Под ред. Г. А. Щекутьева. М.: Антидор, 2001. 236 с.
- Kislitsyn A.A., Kozlova A.B., Masherov E.L., Orlov Yu.N. Numerical Algorithm for Self-Consistent Stationary Level for Multidimensional Non-Stationary Time-Series. Keldysh Inst. Prepr. M., 2017. № 124. 14 p.
- The Fourier Transform in Biomedical Engineering. T.M. Peters, J. Williams (Eds.). Basel: Birkhäuser, 1998. 199 p.
- Kolmogoroff A.N. Sulla determinazione empirica di una legge di distribuzione // Giornale Ist. Italiano degly Attuari. 1933. V. 4. № 1. P. 83–91.
- Гнеденко Б.В. Курс теории вероятностей. М.: Физматлит, 1961. 406 с.
- Кислицын А.А., Козлова А.Б., Корсакова М.Б., Машеров Е.Л., Орлов Ю.Н. Стационарная точка уровня значимости для нестационарных функций распределения. Препр. ИПМ им. М.В. Келдыша. М., 2018. № 113. 20 с.
- Smolyanov O.G., Weizsacker H., Wittin O. Chernoff’s Theorem and Discrete time Approximation of Brownian Motion on Manifolds // Potential Anal. 2007. V. 26. P. 1–29.
- Орлов Ю.Н., Сакбаев В.Ж., Смолянов О.Г. Формулы Фейнмана как метод усреднения случайных гамильтонианов // Тр. Мат. ин-та РАН. 2014. Т. 285. С. 232–243.
- Бутко Я.А., Смолянов О.Г. Формулы Фейнмана в стохастической и квантовой динамике. В сб.: Современные проблемы математики и механики. М., 2011. Т. 6. № 1. С. 61–75.
Supplementary files
