Return Interval Statistics of Extremes in Multiplicative Cascade Model: An Analytical Approach
- 1 кафедра радиотехнических систем, СПбГЭТУ «ЛЭТИ» им. В.И. Ульянова (Ленина)
- 2 к.т.н., докторант, кафедра радиотехнических систем, СПбГЭТУ «ЛЭТИ» им. В.И. Ульянова (Ленина)
- 3 аспирант, ассистент, кафедра радиотехнических систем, СПбГЭТУ «ЛЭТИ» им. В.И. Ульянова (Ленина)
- 4 к.б.н., ст. преподаватель, кафедра водоснабжения и водоотведения, ФГОУ ВПО «Казанский государственный архитектурно-строительный университет»
Abstract
In the last decade, multiplicative cascades have been introduced as an efficient tool to simulate data with nonlinear long-range dependence that can be observed very broadly in nature, including many processes and structures in biology and physiology. In has been shown that this long-range dependence affects significantly return interval statistics leading to broader probability density functions and pronounced conditional memory. Recently several tools aiming at predicting extremes in physiological records that may lead to undesirable physiological conditions and implementation of biofeedback algorithms to avoid them that utilize the return interval approach have been suggested. Finite size effect appears as a limitation for the available solutions based on finite data simulations. The paper suggests an analytical functional form that is capable of describing the probability density function of return intervals in a deterministic multiplicative cascade model for any given threshold level and data length. It is also shown that this functional form remains valid in the randomized multiplicative cascade that is the most common general model representing nonlinear long-range memory in biological and physiological data. The solution aims at overcoming finite size limitations in applications related to prediction and biofeedback utilizing the return interval approach.
How to cite
Маркелов О.А., Богачев М.И., Соколова А.А., Каюмов А.Р. Аналитическое решение задачи интервальных статистик выбросов для модели мультипликативного каскада // Биомедицинская радиоэлектроника. 2012. № 1. С. 45–48.
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