Let 1 < p <∞ and n ≥ 2. The authors establish the L p (ℝ n+1 ) boundedness for a class of parabolic singular integral operators with rough kernels. MR(2000) Subject Classification: 42B20; 42B25.

In this paper, we propose a new stochastic volatility model based on a generalized skew-Student-t distribution for stock returns. This new model allows a parsimonious and flexible treatment of the skewness and heavy tails in the conditional distribution of the returns. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for computing the posterior estimates of the model parameters. Value-at-Risk (VaR) and Expected Shortfall (ES) forecasting via a computational Bayesian framework are considered. The MCMC-based method exploits a skewnormal mixture representation of the error distribution. The proposed methodology is applied to the Shenzhen Stock Exchange Component Index (SZSE-CI) daily returns. Bayesian model selection criteria reveal that there is a significant improvement in model fit to the SZSE-CI returns data by using the SV model based on a generalized skew-Student-t distribution over the usual normal and Student-t models. Empirical results show that the skewness can improve VaR and ES forecasting in comparison with the normal and Student-t models. We demonstrate that the generalized skew-Studentt tail behavior is important in modeling stock returns data.

Abstract. In this paper the authors study the L p boundedness for parabolic Littlewood-Paley operatorwhereand Ω satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

In this paper, a new statistical method to deal with the quantum finance is proposed. Through analyzing the stock data of China Mobile Communication Corporation, we discover its quantum financial effect, and then we innovate the method of testing the existence of the quantum financial effect. Furthermore, the classical normal process of the Glosten-Jagannathan-Runkle (GJR) model has been changed into the quantum wave-function distribution, which is based on the 'one-dimensional infinitely deep square potential well'. The research shows that the quantum GJR model can reveal the interior uncertainty of the financial market and has a better prediction availability.

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