A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differen...A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved展开更多
The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, und...The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.展开更多
In measuring the trade process in a double auction (DA) market, there is not any observable criterion that is able to describe the matching pairs and their transaction order dynamically. In this paper, we propose a ne...In measuring the trade process in a double auction (DA) market, there is not any observable criterion that is able to describe the matching pairs and their transaction order dynamically. In this paper, we propose a new observable criterion called Marshallian deviation. It can be used to measure the distance of a transaction path deviating from the Marshallian path mathematically, and to answer the question why buyers with high values will trade with sellers with low costs in advance in some types of DA but not in others. Furthermore, three factors influencing the Marshallian deviations both in the CDA and in the PDA are also studied. They are respectively the strategic algorithm, the transaction duration and the number of traders. A few interesting findings are presented.展开更多
In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased est...In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.展开更多
文摘A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved
基金Project supported by the National Natural Science Foundation of China
文摘The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.
基金This research is supported by the National Natural Science Foundation of China, CAS, MADIS and RGC of Hong Kong.
文摘In measuring the trade process in a double auction (DA) market, there is not any observable criterion that is able to describe the matching pairs and their transaction order dynamically. In this paper, we propose a new observable criterion called Marshallian deviation. It can be used to measure the distance of a transaction path deviating from the Marshallian path mathematically, and to answer the question why buyers with high values will trade with sellers with low costs in advance in some types of DA but not in others. Furthermore, three factors influencing the Marshallian deviations both in the CDA and in the PDA are also studied. They are respectively the strategic algorithm, the transaction duration and the number of traders. A few interesting findings are presented.
基金supported by National Natural Science Foundation of China(Grant Nos.11201452 and 11271346)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402120017)the Fundamental Research Funds for the Central Universities(Grant No.WK0010000052)
文摘In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.
