Multifractals can be defined as fractal systems that express a range of fractal dimensions. The origins of multifractality in time series data have conventionally been attributed to fat-tailed probability distributions, and to long-range correlations. Multifractal sequences can be generated from...

Although an economy is influenced by a natural disaster, the market response to the disaster during the first 24 hours is not clearly understood. Here we show that an earthquake quickly causes temporal changes in a foreign exchange market by examining the case of the Tohoku-Oki earthquake....

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper, we generalize the model of interevent time to reproduce a variety of self-affine time...

We introduce the stochastic multiplicative point process modeling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f)∝1/fβ, scaled as power of frequency for various values of β between 0.5 and 2. Furthermore, we analyze the relation between the...

Starting from the developed generalized point process model of 1/f noise [B. Kaulakys et al., Phys. Rev. E 71 (2005) 051105] we derive the nonlinear stochastic differential equations for the signal exhibiting 1/fβ noise and 1/xλ distribution density of the signal intensity with different...

We propose a method of estimating network structures only from observed marked point processes using the multi-dimensional scaling. In this method, first, we calculate a spike time metric which quantifies a metric distance between the observed marked point processes. Next, to represent a...

We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity...

The Weibull distribution is proposed as a model for response times. Theoretical support is offered by classical results for extreme-value distributions. Fits of the Weibull distribution to response time data in different contexts show that this distribution (and the exponential distribution on...

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal...

We present a cognitive model, based on the mathematical theory of point processes, which extends the results of two studies by Johansen (Physica A 276 (2000) 338; Physica A 296 (2001) 539) on download relaxation dynamics. Responses from subjects are considered as single events, which are received...