Bronislovas Kaulakys

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We present a simple point process model of 1/f(beta) noise, covering different values of the exponent beta . The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence, or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some(More)
Probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this article we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions(More)
Starting from the simple point process model of 1/f noise, we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise, in any desirably wide range of frequency. A stochastic differential equation (the general Langevin equation with a multiplicative noise) that gives 1/f noise is derived. The solution of the equation exhibits(More)
The problem of the intrinsic origin of 1=f noise is considered. Currents and signals consisting of a sequence of pulses are analyzed. It is shown that the intrinsic origin of 1=f noise is a random walk of the average time between subsequent pulses of the pulse sequence, or the interevent time. This results in the long-memory process for the pulse occurrence(More)
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ∝ 1/f , scaled as power of frequency for various values of β between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law(More)
An analytically solvable model is proposed exhibiting 1/f spectrum in any desirably wide range of frequency (but excluding the point f = 0). The model consists of pulses whose recurrence times obey an autoregressive process with very small damping. PACS: 05.40.+j, 02.50.-r, 72.70.+m
Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an autoregressive process with very small damping. The power spectrum of the process can be expressed by the Hooge formula. The(More)
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 description of the trading activities with the same parameters(More)