Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index
نویسندگان
چکیده
منابع مشابه
The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst parameter H requires sophisticated techniques that often yield ambiguous results. In this work we show that fBm series map into a scale free visibility grap...
متن کاملAre fractional Brownian motions predictable?
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. Mathematics Subject Classification (2000). Primary 60G07; Secondary 60G15, 60G48, 60G25.
متن کاملAnalytical properties of horizontal visibility graphs in the Feigenbaum scenario.
Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-do...
متن کاملTime reversal for drifted fractional Brownian motion with Hurst index H > 1/2
Let X be a drifted fractional Brownian motion with Hurst index H > 1/2. We prove that there exists a fractional backward representation of X , i.e. the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2. We then apply our result to stochastic differential equations driven b...
متن کامل9 Are fractional Brownian motions predictable ?
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. 1 Intoduction The question in the title is provocative, of course. Everybody familiar with the theory of stochast...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica A: Statistical Mechanics and its Applications
سال: 2011
ISSN: 0378-4371
DOI: 10.1016/j.physa.2011.04.020