The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctu...The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. In the overloaded （OL） case, the asymptotic variability is studied for five performance measures： queue length, workload, busy time, idle time and number of departures. The proof is based on strong approximations, which approximate discrete performance processes with （reflected） Brownian motions. We conduct numerical examples to provide insights on these LIL results.展开更多
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
It is often important to incorporate covariate information in the design of clinical trials. In literature there are many designs of using stratification and covariate-adaptive randomization to balance certain known c...It is often important to incorporate covariate information in the design of clinical trials. In literature there are many designs of using stratification and covariate-adaptive randomization to balance certain known covariate. Recently, some covariate-adjusted response-adaptive （CARA） designs have been proposed and their asymptotic properties have been studied （Ann. Statist. 2007）. However, these CARA designs usually have high variabilities. In this paper, a new family of covariate-adjusted response-adaptive （CARA） designs is presented. It is shown that the new designs have less variables and therefore are more efficient.展开更多
RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<su...RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<sub>i</sub>}.In this letter, let {X<sub>i</sub>} be a standard normal sequence of random variables with zero meanand unit variance and write r<sub>ij</sub>=cov（X<sub>i</sub>, X<sub>j</sub>）.展开更多
基金Supported by the National Natural Science Foundation of China(No.11471053)
文摘The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. In the overloaded （OL） case, the asymptotic variability is studied for five performance measures： queue length, workload, busy time, idle time and number of departures. The proof is based on strong approximations, which approximate discrete performance processes with （reflected） Brownian motions. We conduct numerical examples to provide insights on these LIL results.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
基金Partially supported by the National Natural Science Foundation of China (10771192)NSF Awards DMS-0349048 of USA
文摘It is often important to incorporate covariate information in the design of clinical trials. In literature there are many designs of using stratification and covariate-adaptive randomization to balance certain known covariate. Recently, some covariate-adjusted response-adaptive （CARA） designs have been proposed and their asymptotic properties have been studied （Ann. Statist. 2007）. However, these CARA designs usually have high variabilities. In this paper, a new family of covariate-adjusted response-adaptive （CARA） designs is presented. It is shown that the new designs have less variables and therefore are more efficient.
文摘RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<sub>i</sub>}.In this letter, let {X<sub>i</sub>} be a standard normal sequence of random variables with zero meanand unit variance and write r<sub>ij</sub>=cov（X<sub>i</sub>, X<sub>j</sub>）.
