In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common h...In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.展开更多
For the widely orthant dependent （WOD） structure, this paper mainly investigates the precise large deviations for the partial sums of WOD and non-identically distributed random variables with dominatedly varying tai...For the widely orthant dependent （WOD） structure, this paper mainly investigates the precise large deviations for the partial sums of WOD and non-identically distributed random variables with dominatedly varying tails. The obtained results extend some corresponding results.展开更多
Three major elements, carbon, hydrogen, and nitrogen, in twenty-four bituminous coal samples, were measured by laser-induced breakdown spectroscopy. Argon and helium were applied as ambient gas to enhance the signals ...Three major elements, carbon, hydrogen, and nitrogen, in twenty-four bituminous coal samples, were measured by laser-induced breakdown spectroscopy. Argon and helium were applied as ambient gas to enhance the signals and eliminate the interference of nitrogen from surrounding air. The relative standard deviation of the related emission lines and the performance in the partial least squares （PLS） modeling were compared for different ambient environments. The results showed that argon not only improved the intensity, but also reduced signal fluctuation. The PLS model also had the optimal performance in multi-element analysis using argon as ambient gas. The root mean square error of prediction of carbon concentration decreased from 4.25% in air to 3.49% in argon, while the average relative error reduced from 4.96% to 2.98%. Hydrogen line demonstrated similar improvement. Yet, the nitrogen lines were too weak to be detected even in an argon environment which suggested the nitrogen signal measured in air come from the breakdown of nitrogen molecules in the atmosphere.展开更多
Based on slow- and fast-response measurements under neutral stratification conditions from a 325-m meteorological tower located in a built-up area of north-central Beijing as well as a descriptive survey of surface ro...Based on slow- and fast-response measurements under neutral stratification conditions from a 325-m meteorological tower located in a built-up area of north-central Beijing as well as a descriptive survey of surface roughness elements (i.e., buildings and trees) around the tower site, urban roughness lengths, zo, with zero-plane displacement height are estimated using logarithmic wind profile and morphometric methods in eight 45° directional sectors. When comparing their results with each other, the slow-response method tends to give smaller zo values. At a given location, considerable directional variations in values are observed. The effect of surface roughness on urban turbulence characteristics in terms of non-dimensional standard deviations of three-component velocity, σi/u*1 (where i = u, v, w and u*1 is local friction velocity), is investigated.展开更多
We prove large deviation results on the partial and random sums s n =Σ i=1 n X i , n?1; S(t)=Σ i=1 N(t) X i , t?0, where {N(t);t?0} are non-negative integer-valued random variables and {X n ;n?1} are independent non...We prove large deviation results on the partial and random sums s n =Σ i=1 n X i , n?1; S(t)=Σ i=1 N(t) X i , t?0, where {N(t);t?0} are non-negative integer-valued random variables and {X n ;n?1} are independent non-negative random variables with distribution, F n , of X n , independent of {N(t);t?0}. Special attention is paid to the distribution of dominated variation.展开更多
We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting r...We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.展开更多
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large devi...M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.展开更多
Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normaliz...Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.展开更多
The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.展开更多
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random pro...Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.展开更多
This contribution is dedicated to the modeling of the end-wall flows in a throughflow model for turbomachinery applications. The throughflow model is based on the Euler or Navier-Stokes equations solved by a Finite-Vo...This contribution is dedicated to the modeling of the end-wall flows in a throughflow model for turbomachinery applications. The throughflow model is based on the Euler or Navier-Stokes equations solved by a Finite-Volume technique. Two approaches are presented for the end-wall modeling. The first one is based on an inviscid formulation with dedicated 3-D distributions of loss coefficient and deviation in the end-wall regions. The second approach is directly based on a viscous formulation with no-slip boundary condition along the annular end-walls and blade force modification in the region close to the end-walls. The throughflow results are compared to a series of 3-D Navier-Stokes calculations averaged in the circumferential direction. These 3-D calculations were performed on the three rotors of a low pressure axial compressor, for a series of tip clearance values.展开更多
In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, L...In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081) .
文摘In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
文摘For the widely orthant dependent （WOD） structure, this paper mainly investigates the precise large deviations for the partial sums of WOD and non-identically distributed random variables with dominatedly varying tails. The obtained results extend some corresponding results.
基金Acknowledgements The authors are grateful for the financial support from the National Natural Science Foundation of China （Grant No. 51061130536）.
文摘Three major elements, carbon, hydrogen, and nitrogen, in twenty-four bituminous coal samples, were measured by laser-induced breakdown spectroscopy. Argon and helium were applied as ambient gas to enhance the signals and eliminate the interference of nitrogen from surrounding air. The relative standard deviation of the related emission lines and the performance in the partial least squares （PLS） modeling were compared for different ambient environments. The results showed that argon not only improved the intensity, but also reduced signal fluctuation. The PLS model also had the optimal performance in multi-element analysis using argon as ambient gas. The root mean square error of prediction of carbon concentration decreased from 4.25% in air to 3.49% in argon, while the average relative error reduced from 4.96% to 2.98%. Hydrogen line demonstrated similar improvement. Yet, the nitrogen lines were too weak to be detected even in an argon environment which suggested the nitrogen signal measured in air come from the breakdown of nitrogen molecules in the atmosphere.
文摘Based on slow- and fast-response measurements under neutral stratification conditions from a 325-m meteorological tower located in a built-up area of north-central Beijing as well as a descriptive survey of surface roughness elements (i.e., buildings and trees) around the tower site, urban roughness lengths, zo, with zero-plane displacement height are estimated using logarithmic wind profile and morphometric methods in eight 45° directional sectors. When comparing their results with each other, the slow-response method tends to give smaller zo values. At a given location, considerable directional variations in values are observed. The effect of surface roughness on urban turbulence characteristics in terms of non-dimensional standard deviations of three-component velocity, σi/u*1 (where i = u, v, w and u*1 is local friction velocity), is investigated.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.10071058,70273209) the Ministry of Education of China.The authors are grateful to the referees for their comments and suggestions,which led to the present imp
文摘We prove large deviation results on the partial and random sums s n =Σ i=1 n X i , n?1; S(t)=Σ i=1 N(t) X i , t?0, where {N(t);t?0} are non-negative integer-valued random variables and {X n ;n?1} are independent non-negative random variables with distribution, F n , of X n , independent of {N(t);t?0}. Special attention is paid to the distribution of dominated variation.
基金The author is grateful to the referees for their comments and suggestions. This work was supported by the National Natural Science Foundation of China and the Ministry of Education of China.
文摘We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function.For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
基金supported by National Natural Science Foundation of China (Grants Nos. 11401590 and 11571052)
文摘Let(Z_n) be a supercritical branching process with immigration in a random environment. Firstly, we prove that under a simple log moment condition on the offspring and immigration distributions, the naturally normalized population size W_n converges almost surely to a finite random variable W. Secondly, we show criterions for the non-degeneracy and for the existence of moments of the limit random variable W. Finally, we establish a central limit theorem, a large deviation principle and a moderate deviation principle about log Z_n.
文摘The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
基金Research supported by NSFC(No.10271091,10571139)
文摘Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.
文摘This contribution is dedicated to the modeling of the end-wall flows in a throughflow model for turbomachinery applications. The throughflow model is based on the Euler or Navier-Stokes equations solved by a Finite-Volume technique. Two approaches are presented for the end-wall modeling. The first one is based on an inviscid formulation with dedicated 3-D distributions of loss coefficient and deviation in the end-wall regions. The second approach is directly based on a viscous formulation with no-slip boundary condition along the annular end-walls and blade force modification in the region close to the end-walls. The throughflow results are compared to a series of 3-D Navier-Stokes calculations averaged in the circumferential direction. These 3-D calculations were performed on the three rotors of a low pressure axial compressor, for a series of tip clearance values.
基金Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China
文摘In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.
