Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partia...Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.展开更多
In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather ar...In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables展开更多
We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some re...We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved展开更多
Let {Xn,n 1) be a sequence of mixing random variables, S(n)S, >0, d=1 or-1.This note investigates that where is an arbitrary but fixed positive number. As application we give some results on the convergence rates...Let {Xn,n 1) be a sequence of mixing random variables, S(n)S, >0, d=1 or-1.This note investigates that where is an arbitrary but fixed positive number. As application we give some results on the convergence rates for randomly indexed partial sums. Some known results are extended and generalized.展开更多
In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.
This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previou...This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.展开更多
In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special c...In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results.展开更多
Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2（log2{X}）^2〈∞and φ（n）=O（1/log n）^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O（√n/（log2n）^γ for some γ〉1/2.We prove ...Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2（log2{X}）^2〈∞and φ（n）=O（1/log n）^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O（√n/（log2n）^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP（｜Sn｜≥ε√ESn^2log2n＋an）=√2.The results of Gut and Spataru （2000） are special cases of ours.展开更多
Let {X,X1,X2,……}be a zero mean strictly stationary Ф-mixing sequence. Set Sn=∑n k=1 and f（x^p）=∑∞n=1 n^r-2P（｜Sn｜≥x^p√ES2nlog n）,When ε〉（√2）1/p,for p〉1/2 and r〉1,the conditions for ∫∞ε f（x^p）...Let {X,X1,X2,……}be a zero mean strictly stationary Ф-mixing sequence. Set Sn=∑n k=1 and f（x^p）=∑∞n=1 n^r-2P（｜Sn｜≥x^p√ES2nlog n）,When ε〉（√2）1/p,for p〉1/2 and r〉1,the conditions for ∫∞ε f（x^p）dx 〈∞ to hold is established, by using coupled methods together withstrong approximation, which are different from the traditional symmetrization and Hoffman-JФrgensen inequality.展开更多
文摘Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.
文摘In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables
基金supported by National Natural Science Foundation of China(Grant Nos. 11171303 and 60974006)the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)the Natural Science Foundation of Zhejiang Province(Grant No.Y6100176)
文摘We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved
文摘Let {Xn,n 1) be a sequence of mixing random variables, S(n)S, >0, d=1 or-1.This note investigates that where is an arbitrary but fixed positive number. As application we give some results on the convergence rates for randomly indexed partial sums. Some known results are extended and generalized.
基金The NSF (10571073) of China985 Program of Jilin University
文摘In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.
文摘This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.
文摘In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results.
基金National Natural Science Foundation of China (No.10571159)
文摘Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2（log2{X}）^2〈∞and φ（n）=O（1/log n）^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O（√n/（log2n）^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP（｜Sn｜≥ε√ESn^2log2n＋an）=√2.The results of Gut and Spataru （2000） are special cases of ours.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10771192 and 10671176) 1)
文摘Let {X,X1,X2,……}be a zero mean strictly stationary Ф-mixing sequence. Set Sn=∑n k=1 and f（x^p）=∑∞n=1 n^r-2P（｜Sn｜≥x^p√ES2nlog n）,When ε〉（√2）1/p,for p〉1/2 and r〉1,the conditions for ∫∞ε f（x^p）dx 〈∞ to hold is established, by using coupled methods together withstrong approximation, which are different from the traditional symmetrization and Hoffman-JФrgensen inequality.
