9 research outputs found
Analysis of Non-stationary Data for Heart-Rate Fluctuations in Terms of Drift and Diffusion Coefficients
We describe a method for analyzing the stochasticity in the non-stationary
data for the beat-to-beat fluctuations in the heart rates of healthy subjects,
as well as those with congestive heart failure. The method analyzes the returns
time series of the data as a Markov process, and computes the Markov time
scale, i.e., the time scale over which the data are a Markov process. We also
construct an effective stochastic continuum equation for the return series. We
show that the drift and diffusion coefficients, as well as the amplitude of the
returns time series for healthy subjects are distinct from those with CHF.
Thus, the method may potentially provide a diagnostic tool for distinguishing
healthy subjects from those with congestive heart failure, as it can
distinguish small differences between the data for the two classes of subjects
in terms of well-defined and physically-motivated quantities.Comment: 6 pages, two columns, 6 figure
Statistical Properties of the Interbeat Interval Cascade in Human Subjects
Statistical properties of interbeat intervals cascade are evaluated by
considering the joint probability distribution for two interbeat increments and of
different time scales and . We present evidence that the
conditional probability distribution
may obey a Chapman-Kolmogorov equation. The corresponding Kramers-Moyal (KM)
coefficients are evaluated. It is shown that while the first and second KM
coefficients, i.e., the drift and diffusion coefficients, take on well-defined
and significant values, the higher-order coefficients in the KM expansion are
very small. As a result, the joint probability distributions of the increments
in the interbeat intervals obey a Fokker-Planck equation. The method provides a
novel technique for distinguishing the two classes of subjects in terms of the
drift and diffusion coefficients, which behave differently for two classes of
the subjects, namely, healthy subjects and those with congestive heart failure.Comment: 5 pages, 6 figure
Uncertainty in the Fluctuations of the Price of Stocks
We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as
an emerging market that has been affected by several political crises during
the recent years, and analyze the non-Gaussian probability density function
(PDF) of the log returns of the stocks' prices. We show that while the average
of the index did not fall very much over the time period of the study, its
day-to-day fluctuations strongly increased due to the crises. Using an approach
based on multiplicative processes with a detrending procedure, we study the
scale-dependence of the non-Gaussian PDFs, and show that the temporal
dependence of their tails indicates a gradual and systematic increase in the
probability of the appearance of large increments in the returns on approaching
distinct critical time scales over which the TEPIX has exhibited maximum
uncertainty.Comment: 5 pages, 5 figures. Accepted to appear in IJMP
Uncertainty in the Fluctuations of the Price of Stocks
Abstract We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty. PACS number(s): 89.65.Gh, 89.75.-k
Markov Properties of Electrical Discharge Current Fluctuations in Plasma
Using the Markovian method, we study the stochastic nature of electrical
discharge current fluctuations in the Helium plasma. Sinusoidal trends are
extracted from the data set by the Fourier-Detrended Fluctuation analysis and
consequently cleaned data is retrieved. We determine the Markov time scale of
the detrended data set by using likelihood analysis. We also estimate the
Kramers-Moyal's coefficients of the discharge current fluctuations and derive
the corresponding Fokker-Planck equation. In addition, the obtained Langevin
equation enables us to reconstruct discharge time series with similar
statistical properties compared with the observed in the experiment. We also
provide an exact decomposition of temporal correlation function by using
Kramers-Moyal's coefficients. We show that for the stationary time series, the
two point temporal correlation function has an exponential decaying behavior
with a characteristic correlation time scale. Our results confirm that, there
is no definite relation between correlation and Markov time scales. However
both of them behave as monotonic increasing function of discharge current
intensity. Finally to complete our analysis, the multifractal behavior of
reconstructed time series using its Keramers-Moyal's coefficients and original
data set are investigated. Extended self similarity analysis demonstrates that
fluctuations in our experimental setup deviates from Kolmogorov (K41) theory
for fully developed turbulence regime.Comment: 25 pages, 9 figures and 4 tables. V3: Added comments, references,
figures and major correction
Uncertainty in the Fluctuations of the Price of Stocks
We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.