55 research outputs found
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
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
Consentaneous agent-based and stochastic model of the financial markets
We are looking for the agent-based treatment of the financial markets
considering necessity to build bridges between microscopic, agent based, and
macroscopic, phenomenological modeling. The acknowledgment that agent-based
modeling framework, which may provide qualitative and quantitative
understanding of the financial markets, is very ambiguous emphasizes the
exceptional value of well defined analytically tractable agent systems. Herding
as one of the behavior peculiarities considered in the behavioral finance is
the main property of the agent interactions we deal with in this contribution.
Looking for the consentaneous agent-based and macroscopic approach we combine
two origins of the noise: exogenous one, related to the information flow, and
endogenous one, arising form the complex stochastic dynamics of agents. As a
result we propose a three state agent-based herding model of the financial
markets. From this agent-based model we derive a set of stochastic differential
equations, which describes underlying macroscopic dynamics of agent population
and log price in the financial markets. The obtained solution is then subjected
to the exogenous noise, which shapes instantaneous return fluctuations. We test
both Gaussian and q-Gaussian noise as a source of the short term fluctuations.
The resulting model of the return in the financial markets with the same set of
parameters reproduces empirical probability and spectral densities of absolute
return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our
result confirms the prevalent idea in behavioral finance that herding
interactions may be dominant over agent rationality and contribute towards
bubble formation.Comment: 17 pages, 6 figures, Gontis V, Kononovicius A (2014) Consentaneous
Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7):
e102201. doi: 10.1371/journal.pone.010220
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
Point Processes Modeling of Time Series Exhibiting Power-Law Statistics
We consider stochastic point processes generating time series exhibiting
power laws of spectrum and distribution density (Phys. Rev. E 71, 051105
(2005)) and apply them for modeling the trading activity in the financial
markets and for the frequencies of word occurrences in the language.Comment: 4 pages, 2 figure
Point Process Models of 1/f Noise and Internet Traffic
We present a simple model reproducing the long-range autocorrelations and the
power spectrum of the web traffic. The model assumes the traffic as Poisson
flow of files with size distributed according to the power-law. In this model
the long-range autocorrelations are independent of the network properties as
well as of inter-packet time distribution.Comment: 6 pages, 2 figures, CNET2004 Proceedings AI
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