A novel method to characterize CMOS process fluctuations in subthreshold current mirrors （SCM） is reported. The proposed model is succinct in methodology and calculation complexity compared with previous statistical...A novel method to characterize CMOS process fluctuations in subthreshold current mirrors （SCM） is reported. The proposed model is succinct in methodology and calculation complexity compared with previous statistical models. However,it provides favorable estimations of CMOS process fluctuations on the SCM circuit, which makes it promising for engineering applications. The model statistically abstracts physical parameters, which depend on the IC process, into random variables with certain mean values and standard deviations, while aggregating all the random impacts into a discrete martingale. The correctness of the proposed method is experimentally verified on an SCM circuit implemented in an SMIC 0.18μm CMOS 1P6M mixed signal process with a conversion factor of 100 in an input range from 100pA to lμA. The pro- posed theory successfully predicts - 10% of die-to-die fluctuation measured in the experiment, and also suggests the -lmV of threshold voltage standard deviation over a single die,which meets the process parameters suggested by the design kit from the foundry. The deviations between calculated probabilities and measured data are less than 8%. Meanwhile, pertinent suggestions concerning high fluctuation tolerance subthreshold analog circuit design are also made and discussed.展开更多
Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determin...Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.展开更多
A reliability based analysis method for a drilled shaft stabilized slope system is presented in this paper. The drilled shaft stabilization mechanisms for the slope were treated as the drilled shaft induced soil archi...A reliability based analysis method for a drilled shaft stabilized slope system is presented in this paper. The drilled shaft stabilization mechanisms for the slope were treated as the drilled shaft induced soil arching, which was quantified by the load transfer factor in the limited equilibrium analysis. However, due to the inherent uncertainties of the soil properties and the model error of the semi-empirical load transfer equation, an extension modification of the deterministic method into a probabilistic method is developed in this paper. The MCS （Monte Carlo simulation） with log-normal random variables has been employed to calculate the probability of failure （Pf） for the drilled shafts/slope system. The developed theories were coded into a computer program for analyzing complex slope geometry and slope profile conditions. Finally, a case study has been performed to illustrate the application analysis of the developed probability approach in drilled shafts/slope system.展开更多
This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables, and obtains some results on these r.v.s' precise moderate deviations with random c...This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables, and obtains some results on these r.v.s' precise moderate deviations with random centralizing constants, which extend the boundary γλ(t)of large deviations to γ(λ(t)^1/s,whereγ>0,1<s<2,λ(t)is the expectation of the random index N(t),t>0.展开更多
Abstract Let X1, X2,... be a sequence of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequence {X...Abstract Let X1, X2,... be a sequence of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequence {Xk, k 〉 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities Sn = fi Xk and S（n） =∑ k=1 n 〉 1, and their randomized versions ST and S（τ） are studied. Some risk theory are presented. max Sk for 1〈k〈n applications to the展开更多
Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple coro...Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker.展开更多
Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ：...Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ： k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P（X〉x）/P（τ〉x）→0 as x →∞.展开更多
The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts.Existing methods are either compu...The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts.Existing methods are either computationally unaffordable or with limited application scope.Accordingly,a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed.The fuzziness propagation in the random reliability,which is the focus of the present study,is performed by the proposed method,in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation.First-Order,Second-Moment(FOSM)method which can be replaced by its counterparts is utilized to calculate the structural random reliability.Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.展开更多
Let {Xt,t ≥ 0} be a Levy process with Levy measure v on （-∞,∞）, and let τ be a nonnegative random variable independent of {Xt,t ≥ 0}. We are interested in the tail probabilities of Xτ and X（τ） = sup0≤t≤τ...Let {Xt,t ≥ 0} be a Levy process with Levy measure v on （-∞,∞）, and let τ be a nonnegative random variable independent of {Xt,t ≥ 0}. We are interested in the tail probabilities of Xτ and X（τ） = sup0≤t≤τ Xt. For various cases, under the assumption that either the Levy measure v or the random variable T has a heavy right tail we prove that both Pr（XT 〉 x） and Pr（X（τ） 〉 x） are asymptotic to ETv（（x, ∞）） ＋ Pτ（τ 〉 x/（0 V EX1）） as x → ∞, where Pr（τ 〉 x/x） = 0 by convention.展开更多
文摘A novel method to characterize CMOS process fluctuations in subthreshold current mirrors （SCM） is reported. The proposed model is succinct in methodology and calculation complexity compared with previous statistical models. However,it provides favorable estimations of CMOS process fluctuations on the SCM circuit, which makes it promising for engineering applications. The model statistically abstracts physical parameters, which depend on the IC process, into random variables with certain mean values and standard deviations, while aggregating all the random impacts into a discrete martingale. The correctness of the proposed method is experimentally verified on an SCM circuit implemented in an SMIC 0.18μm CMOS 1P6M mixed signal process with a conversion factor of 100 in an input range from 100pA to lμA. The pro- posed theory successfully predicts - 10% of die-to-die fluctuation measured in the experiment, and also suggests the -lmV of threshold voltage standard deviation over a single die,which meets the process parameters suggested by the design kit from the foundry. The deviations between calculated probabilities and measured data are less than 8%. Meanwhile, pertinent suggestions concerning high fluctuation tolerance subthreshold analog circuit design are also made and discussed.
基金the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)the Scientific Program of Department of Education of Jiangxi Province of China(Grant No.GJJ190732)。
基金the Shanghai Science and Technology Commission, No. 01ZA14003.
文摘Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
文摘A reliability based analysis method for a drilled shaft stabilized slope system is presented in this paper. The drilled shaft stabilization mechanisms for the slope were treated as the drilled shaft induced soil arching, which was quantified by the load transfer factor in the limited equilibrium analysis. However, due to the inherent uncertainties of the soil properties and the model error of the semi-empirical load transfer equation, an extension modification of the deterministic method into a probabilistic method is developed in this paper. The MCS （Monte Carlo simulation） with log-normal random variables has been employed to calculate the probability of failure （Pf） for the drilled shafts/slope system. The developed theories were coded into a computer program for analyzing complex slope geometry and slope profile conditions. Finally, a case study has been performed to illustrate the application analysis of the developed probability approach in drilled shafts/slope system.
基金This research is supported by National Science Foundation of China (No. 10271087).
文摘This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables, and obtains some results on these r.v.s' precise moderate deviations with random centralizing constants, which extend the boundary γλ(t)of large deviations to γ(λ(t)^1/s,whereγ>0,1<s<2,λ(t)is the expectation of the random index N(t),t>0.
基金supported by the National Natural Science Foundation of China (No. 11171179)the Research Fund for the Doctoral Program of Higher Education of China (No. 20093705110002)
文摘Abstract Let X1, X2,... be a sequence of dependent and heavy-tailed random variables with distributions F1, F2,.. on （-∞,∞）, and let T be a nonnegative integer-valued random variable independent of the sequence {Xk, k 〉 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities Sn = fi Xk and S（n） =∑ k=1 n 〉 1, and their randomized versions ST and S（τ） are studied. Some risk theory are presented. max Sk for 1〈k〈n applications to the
文摘Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number for B-valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker.
基金Project supported by the National Natural Science Foundation of China(No.11071182)
文摘Let （X, Xk ： k ≥ 1） be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 〉 0.Let τ be a nonnegative integer-valued random variable, independent of {X, Xk ： k ≥ 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums Sτ=∑n=1^τ Xn to have a consistently varying tail when the random number τ has a heavier tail than the summands, i.e.,P（X〉x）/P（τ〉x）→0 as x →∞.
基金supported by the Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)‘111’Pro-ject(Grant No.B07009)the National Natural Science Foundation of China(Grant No.90816024)
文摘The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts.Existing methods are either computationally unaffordable or with limited application scope.Accordingly,a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed.The fuzziness propagation in the random reliability,which is the focus of the present study,is performed by the proposed method,in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation.First-Order,Second-Moment(FOSM)method which can be replaced by its counterparts is utilized to calculate the structural random reliability.Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.
基金supported by National Natural Science Foundation of China(Grant Nos. 10971157,11001209,70871104)the Scientific Research Foundation for the Returned Overseas Chinese Scholars
文摘Let {Xt,t ≥ 0} be a Levy process with Levy measure v on （-∞,∞）, and let τ be a nonnegative random variable independent of {Xt,t ≥ 0}. We are interested in the tail probabilities of Xτ and X（τ） = sup0≤t≤τ Xt. For various cases, under the assumption that either the Levy measure v or the random variable T has a heavy right tail we prove that both Pr（XT 〉 x） and Pr（X（τ） 〉 x） are asymptotic to ETv（（x, ∞）） ＋ Pτ（τ 〉 x/（0 V EX1）） as x → ∞, where Pr（τ 〉 x/x） = 0 by convention.
