102 research outputs found
Trading activity as driven Poisson process: comparison with empirical data
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 applicable for all stocks.Comment: 9 pages, 5 figures, proceedings of APFA
Nonlinear stochastic models of 1/f noise and power-law distributions
Starting from the developed generalized point process model of noise
(B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive
the nonlinear stochastic differential equations for the signal exhibiting
1/f^{\beta}1/x^{\lambda}\beta\lambda1/f^{\beta}$ are demonstrated by the numerical solution of the derived
equations with the appropriate restriction of the diffusion of the signal in
some finite interval. The proposed consideration may be used for modeling and
analysis of stochastic processes in different systems with the power-law
distributions, long-range memory or with the elements of self-organization.Comment: 6 pages, 6 figures, presented at the 3rd NEXT-SigmaPhi International
Conference (13-18 August 2005, Kolymbari CRETE
Modelling financial markets by the multiplicative sequence of trades
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**beta, scaled as power of frequency for various values of
beta between 0.5 and 2. Furthermore, we analyze the relation between the
power-law autocorrelations and the origin of the power-law probability
distribution of the trading activity. The model reproduces the spectral
properties of trading activity and explains the mechanism of power-law
distribution in real markets.Comment: 6 pages, 2 figure
Quantum anti-Zeno effect
Prevention of a quantum system's time evolution by repetitive, frequent
measurements of the system's state has been called the quantum Zeno effect (or
paradox). Here we investigate theoretically and numerically the effect of
repeated measurements on the quantum dynamics of the multilevel systems that
exhibit the quantum localization of the classical chaos. The analysis is based
on the wave function and Schroedinger equation, without introduction of the
density matrix. We show how the quantum Zeno effect in simple few-level systems
can be recovered and understood by formal modeling the measurement effect on
the dynamics by randomizing the phases of the measured states. Further the
similar analysis is extended to investigate of the dynamics of multilevel
systems driven by an intense external force and affected by frequent
measurement. We show that frequent measurements of such quantum systems results
in the delocalization of the quantum suppression of the classical chaos. This
result is the opposite of the quantum Zeno effect. The phenomenon of
delocalization of the quantum suppression and restoration of the classical-like
time evolution of these quasiclassical systems, owing to repetitive frequent
measurements, can therefore be called the 'quantum anti-Zeno effect'. From this
analysis we furthermore conclude that frequently or continuously observable
quasiclassical systems evolve basically in a classical manner.Comment: 12 pages with 2 figure
Fluctuation analysis of the three agent groups herding model
We derive a system of stochastic differential equations simulating the
dynamics of the three agent groups with herding interaction. Proposed approach
can be valuable in the modeling of the complex socio-economic systems with
similar composition of the agents. We demonstrate how the sophisticated
statistical features of the absolute return in the financial markets can be
reproduced by extending the herding interaction of the agents and introducing
the third agent state. As well we consider possible extension of proposed
herding model introducing additional exogenous noise. Such consistent
microscopic and macroscopic model precisely reproduces empirical power law
statistics of the return in the financial markets.Comment: 9 pages, 2 figure
Spurious memory in non-equilibrium stochastic models of imitative behavior
The origin of the long-range memory in the non-equilibrium systems is still
an open problem as the phenomenon can be reproduced using models based on
Markov processes. In these cases a notion of spurious memory is introduced. A
good example of Markov processes with spurious memory is stochastic process
driven by a non-linear stochastic differential equation (SDE). This example is
at odds with models built using fractional Brownian motion (fBm). We analyze
differences between these two cases seeking to establish possible empirical
tests of the origin of the observed long-range memory. We investigate
probability density functions (PDFs) of burst and inter-burst duration in
numerically obtained time series and compare with the results of fBm. Our
analysis confirms that the characteristic feature of the processes described by
a one-dimensional SDE is the power-law exponent of the burst or
inter-burst duration PDF. This property of stochastic processes might be used
to detect spurious memory in various non-equilibrium systems, where observed
macroscopic behavior can be derived from the imitative interactions of agents.Comment: 11 pages, 5 figure
Control of the socio-economic systems using herding interactions
Collective behavior of the complex socio-economic systems is heavily
influenced by the herding, group, behavior of individuals. The importance of
the herding behavior may enable the control of the collective behavior of the
individuals. In this contribution we consider a simple agent-based herding
model modified to include agents with controlled state. We show that in certain
case even the smallest fixed number of the controlled agents might be enough to
control the behavior of a very large system.Comment: 8 pages, 3 figure
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