5,349 research outputs found
Boltzmann-type models with uncertain binary interactions
In this paper we study binary interaction schemes with uncertain parameters
for a general class of Boltzmann-type equations with applications in classical
gas and aggregation dynamics. We consider deterministic (i.e., a priori
averaged) and stochastic kinetic models, corresponding to different ways of
understanding the role of uncertainty in the system dynamics, and compare some
thermodynamic quantities of interest, such as the mean and the energy, which
characterise the asymptotic trends. Furthermore, via suitable scaling
techniques we derive the corresponding deterministic and stochastic
Fokker-Planck equations in order to gain more detailed insights into the
respective asymptotic distributions. We also provide numerical evidences of the
trends estimated theoretically by resorting to recently introduced structure
preserving uncertainty quantification methods
Dynamic evolution of cross-correlations in the Chinese stock market
We study the dynamic evolution of cross-correlations in the Chinese stock
market mainly based on the random matrix theory (RMT). The correlation matrices
constructed from the return series of 367 A-share stocks traded on the Shanghai
Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a
moving window with a size of 400 days. The evolutions of the statistical
properties of the correlation coefficients, eigenvalues, and eigenvectors of
the correlation matrices are carefully analyzed. We find that the stock
correlations are significantly increased in the periods of two market crashes
in 2001 and 2008, during which only five eigenvalues significantly deviate from
the random correlation matrix, and the systemic risk is higher in these
volatile periods than calm periods. By investigating the significant
contributors of the deviating eigenvectors in different moving windows, we
observe a dynamic evolution behavior in business sectors such as IT,
electronics, and real estate, which lead the rise (drop) before (after) the
crashes
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