We consider here quantitative convergence to equilibrium for the kinetic Fokker-Planck equation. We present a weak hypocoercivity approachà la Villani, using weak Poincaré inequality, ensuring subexponential convergence to equilibrium in H 1 sense or in L 2 sense.

The paper considered the sensitivity of unstructured network data to external shocks in the financial system, based on HMM applied in the traditional financial indicator system to construct the new composite index. We integrated economic statistical structure data and internet information, to capture the internal correlation and external shocks to financial markets. There appeared to be some evidence that the new index was superior at measuring the systemic financial risk. In addition, according to the new composite index we constructed, China's systemic financial risk was at the medium high level. It is an important task to prevent the systemic financial risk and maintain the stability of macro-economy. INDEX TERMSSystemic financial risk, Baidu index, hidden Markov model, text mining

This article is concerned with moderate deviation principles of a class of interacting empirical processes. We derive an explicit description of the rate function, and we illustrate these results with Feynman-Kac particle models arising in nonlinear filtering, statistical machine learning, rare event analysis, and computational physics. We discuss functional moderate deviations of the occupation measures for both the strong τ-topology on the space of finite and bounded measures as well as for the corresponding stochastic processes on some class of functions equipped with the uniform topology, yielding the first results of this type for mean field interacting processes. Our approach is based on an original semigroup analysis combined with Orlicz norm inequalities, stochastic perturbation techniques, and projective limit large deviation methods.

Investor behavior is one of the important factors that affects market liquidity. It is very interesting to find out how investor behavior affects stock market liquidity. The Investor sentiment changes and information cognitive ability affect not only their expected returns but also market liquidity through short-selling restrained market behavior. This paper gives a comprehensive index of investor sentiment based on the entropy method. According to the empirical analysis based on evidence from China, we obtain the following results: The investor sentiment has a positive impact on market liquidity; the development of margin trading has curbed the positive impact of investor sentiment on market liquidity; the information cognitive ability has a negative impact on market liquidity; the explosive information volume enhances the market liquidity in the bull, weakens the market liquidity in the bear, and has no significant impact while shocked.

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