The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding c...The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.展开更多
In the past decades, on-line monitoring of batch processes using multi-way independent component analysis （MICA） has received considerable attention in both academia and industry. This paper focuses on two troubleso...In the past decades, on-line monitoring of batch processes using multi-way independent component analysis （MICA） has received considerable attention in both academia and industry. This paper focuses on two troublesome issues concerning selecting dominant independent components without a standard criterion and deter- mining the control limits of monitoring statistics in the presence of non-Gaussian distribution. To optimize the number of key independent components~ we introctuce-anoveiconcept of-system-cleviation, which is ab^e＇io＇evalu[ ate the reconstructed observations with different independent components. The monitored statistics arc transformed to Gaussian distribution data by means of Box-Cox transformation, which helps readily determine the control limits. The proposed method is applied to on-line monitoring of a fed-hatch penicillin fermentation simulator, and the ex- _perimental results indicate the advantages of the improved MICA monitoring compared to the conventional methods.展开更多
Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn ...Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.展开更多
In shield tunneling, the control system needs very reliable capability of deviation rectifying in order to ensure that the tunnel trajectory meets the permissible criterion. To this goal, we present an approach that a...In shield tunneling, the control system needs very reliable capability of deviation rectifying in order to ensure that the tunnel trajectory meets the permissible criterion. To this goal, we present an approach that adopts Markov decision process (MDP) theory to plan the driving force with explicit representation of the uncertainty during excavation. The shield attitudes of possi- ble world and driving forces during excavation are scattered as a state set and an action set, respectively. In particular, an evaluation function is proposed with consideration of the stability of driving force and the deviation of shield attitude. Unlike the deterministic approach, the driving forces based on MDP model lead to an uncertain effect and the attitude is known only with an imprecise probability. We consider the case that the transition probability varies in a given domain estimated by field data, and discuss the optimal policy based on the interval arithmetic. The validity of the approach is discussed by comparing the driving force planning with the actual operating data from the field records of Line 9 in Tianjin. It is proved that the MDP model is reasonable enough to predict the driving force for automatic deviation rectifying.展开更多
Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit t...Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.展开更多
基金National Natural Science Foundation of China (Grant No.60574002)MASCOS grant from Australian Research CouncilNational Natural Science Foundation of China (Grant No.70671018)
文摘The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.
文摘In the past decades, on-line monitoring of batch processes using multi-way independent component analysis （MICA） has received considerable attention in both academia and industry. This paper focuses on two troublesome issues concerning selecting dominant independent components without a standard criterion and deter- mining the control limits of monitoring statistics in the presence of non-Gaussian distribution. To optimize the number of key independent components~ we introctuce-anoveiconcept of-system-cleviation, which is ab^e＇io＇evalu[ ate the reconstructed observations with different independent components. The monitored statistics arc transformed to Gaussian distribution data by means of Box-Cox transformation, which helps readily determine the control limits. The proposed method is applied to on-line monitoring of a fed-hatch penicillin fermentation simulator, and the ex- _perimental results indicate the advantages of the improved MICA monitoring compared to the conventional methods.
基金the National Natural Science Foundation of China(10571001)the Innovation Group Foundation of Anhui University
文摘Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.
基金supported by the National Basic Research Program (973 Program) of China (Grant No. 2007CB714000)
文摘In shield tunneling, the control system needs very reliable capability of deviation rectifying in order to ensure that the tunnel trajectory meets the permissible criterion. To this goal, we present an approach that adopts Markov decision process (MDP) theory to plan the driving force with explicit representation of the uncertainty during excavation. The shield attitudes of possi- ble world and driving forces during excavation are scattered as a state set and an action set, respectively. In particular, an evaluation function is proposed with consideration of the stability of driving force and the deviation of shield attitude. Unlike the deterministic approach, the driving forces based on MDP model lead to an uncertain effect and the attitude is known only with an imprecise probability. We consider the case that the transition probability varies in a given domain estimated by field data, and discuss the optimal policy based on the interval arithmetic. The validity of the approach is discussed by comparing the driving force planning with the actual operating data from the field records of Line 9 in Tianjin. It is proved that the MDP model is reasonable enough to predict the driving force for automatic deviation rectifying.
基金Supported by Shandong Provincial Natural Science Foundation(Grant No.ZR2021MA085)National Natural Science Foundation of China(Grant No.11971063)。
文摘Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.
