1,066 research outputs found
Mass spectrum from stochastic Levy-Schroedinger relativistic equations: possible qualitative predictions in QCD
Starting from the relation between the kinetic energy of a free
Levy-Schroedinger particle and the logarithmic characteristic of the underlying
stochastic process, we show that it is possible to get a precise relation
between renormalizable field theories and a specific Levy process. This
subsequently leads to a particular cut-off in the perturbative diagrams and can
produce a phenomenological mass spectrum that allows an interpretation of
quarks and leptons distributed in the three families of the standard model.Comment: 8 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:1008.425
Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure
Many transport processes in nature exhibit anomalous diffusive properties
with non-trivial scaling of the mean square displacement, e.g., diffusion of
cells or of biomolecules inside the cell nucleus, where typically a crossover
between different scaling regimes appears over time. Here, we investigate a
class of anomalous diffusion processes that is able to capture such complex
dynamics by virtue of a general waiting time distribution. We obtain a complete
characterization of such generalized anomalous processes, including their
functionals and multi-point structure, using a representation in terms of a
normal diffusive process plus a stochastic time change. In particular, we
derive analytical closed form expressions for the two-point correlation
functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let
News and price returns from threshold behaviour and vice-versa: exact solution of a simple agent-based market model
Starting from an exact relationship between news, threshold and price return
distributions in the stationary state, I discuss the ability of the
Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under
normal conditions, this model is not able to transform Gaussian news into
fat-tailed price returns. When the variance of the news so small that only the
players with zero threshold can possibly react to news, this model produces
Levy-distributed price returns with a -1 exponent. In the special case of
super-linear price impact functions, fat-tailed returns are obtained from
well-behaved news.Comment: 4 pages, 3 figures. This is quite possibly the final version. To
appear in J. Phys
Structurally dynamic spin market networks
The agent-based model of stock price dynamics on a directed evolving complex
network is suggested and studied by direct simulation. The stationary regime is
maintained as a result of the balance between the extremal dynamics, adaptivity
of strategic variables and reconnection rules. The inherent structure of node
agent "brain" is modeled by a recursive neural network with local and global
inputs and feedback connections. For specific parametric combination the
complex network displays small-world phenomenon combined with scale-free
behavior. The identification of a local leader (network hub, agent whose
strategies are frequently adapted by its neighbors) is carried out by repeated
random walk process through network. The simulations show empirically relevant
dynamics of price returns and volatility clustering. The additional emerging
aspects of stylized market statistics are Zipfian distributions of fitness.Comment: 13 pages, 5 figures, accepted in IJMPC, references added, minor
changes in model, new results and modified figure
Comment on: Role of Intermittency in Urban Development: A Model of Large-Scale City Formation
Comment to D.H. Zanette and S.C. Manrubia, Phys. Rev. Lett. 79, 523 (1997).Comment: 1 page no figure
Are Financial Crashes Predictable?
We critically review recent claims that financial crashes can be predicted
using the idea of log-periodic oscillations or by other methods inspired by the
physics of critical phenomena. In particular, the October 1997 `correction'
does not appear to be the accumulation point of a geometric series of local
minima.Comment: LaTeX, 5 pages + 1 postscript figur
Statistical properties of absolute log-returns and a stochastic model of stock markets with heterogeneous agents
This paper is intended as an investigation of the statistical properties of
{\it absolute log-returns}, defined as the absolute value of the logarithmic
price change, for the Nikkei 225 index in the 28-year period from January 4,
1975 to December 30, 2002. We divided the time series of the Nikkei 225 index
into two periods, an inflationary period and a deflationary period. We have
previously [18] found that the distribution of absolute log-returns can be
approximated by the power-law distribution in the inflationary period, while
the distribution of absolute log-returns is well described by the exponential
distribution in the deflationary period.\par To further explore these empirical
findings, we have introduced a model of stock markets which was proposed in
[19,20]. In this model, the stock market is composed of two groups of traders:
{\it the fundamentalists}, who believe that the asset price will return to the
fundamental price, and {\it the interacting traders}, who can be noise traders.
We show through numerical simulation of the model that when the number of
interacting traders is greater than the number of fundamentalists, the
power-law distribution of absolute log-returns is generated by the interacting
traders' herd behavior, and, inversely, when the number of fundamentalists is
greater than the number of interacting traders, the exponential distribution of
absolute log-returns is generated.Comment: 12 pages, 5 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
Levy distribution and long correlation times in supermarket sales
Sales data in a commodity market (supermarket sales to consumers) has been
analysed by studying the fluctuation spectrum and noise correlations. Three
related products (ketchup, mayonnaise and curry sauce) have been analysed. Most
noise in sales is caused by promotions, but here we focus on the fluctuations
in baseline sales. These characterise the dynamics of the market. Four hitherto
unnoticed effects have been found that are difficult to explain from simple
econometric models. These effects are: (1) the noise level in baseline sales is
much higher than can be expected for uncorrelated sales events; (2) weekly
baseline sales differences are distributed according to a broad non-Gaussian
function with fat tails; (3) these fluctuations follow a Levy distribution of
exponent alpha = 1.4, similar to financial exchange markets and in stock
markets; and (4) this noise is correlated over a period of 10 to 11 weeks, or
shows an apparent power law spectrum. The similarity to stock markets suggests
that models developed to describe these markets may be applied to describe the
collective behaviour of consumers.Comment: 19 pages, 7 figures, accepted for publication in Physica
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