The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements dis...The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements display severe convergence deterioration in explicit transient heat conduction analysis with lumped heat ca-pacity matrices.This convergence decay is due to the violation of variational integration consistency by the standard Galerkin formulation with lumped heat capacity matrices.This issue is resolved by introducing the boundary-enhanced Galerkin weak form that incorporates the elemental boundary contribution in the discrete finite element formulation.Subsequently,it is theoretically proven that a direct nodal integration identically fulfills the variational integration consistency in the context of the boundary-enhanced Galerkin weak form.The proposed variationally consistent nodal integration therefore enables optimal convergence for explicit transient heat conduction analysis with lumped heat capacity matrices.The efficacy of the proposed variationally con-sistent nodal integration formulation for the 13-node quadrilateral and 39-node hexahedral cubic elements is thoroughly demonstrated via numerical examples.展开更多
Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be depende...Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.展开更多
In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and consta...In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.展开更多
Consider a two-dimensional renewal risk model,in which the claim sizes{Xk;k≥1}form a sequence of i.i.d.copies of a non-negative random vector whose two components are dependent.Suppose that the claim sizes and inter-...Consider a two-dimensional renewal risk model,in which the claim sizes{Xk;k≥1}form a sequence of i.i.d.copies of a non-negative random vector whose two components are dependent.Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d.random pairs,with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large.Then a precise large-deviation formula of the aggregate amount of claims is obtained.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12372201 and 12072302).
文摘The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements display severe convergence deterioration in explicit transient heat conduction analysis with lumped heat ca-pacity matrices.This convergence decay is due to the violation of variational integration consistency by the standard Galerkin formulation with lumped heat capacity matrices.This issue is resolved by introducing the boundary-enhanced Galerkin weak form that incorporates the elemental boundary contribution in the discrete finite element formulation.Subsequently,it is theoretically proven that a direct nodal integration identically fulfills the variational integration consistency in the context of the boundary-enhanced Galerkin weak form.The proposed variationally consistent nodal integration therefore enables optimal convergence for explicit transient heat conduction analysis with lumped heat capacity matrices.The efficacy of the proposed variationally con-sistent nodal integration formulation for the 13-node quadrilateral and 39-node hexahedral cubic elements is thoroughly demonstrated via numerical examples.
基金Supported by the National Natural Science Foundation of China(Nos.11571058&11301481)Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007)+1 种基金Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004)Fundamental Research Funds for the Central Universities(No.DUT17LK31)
文摘Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.
基金Supported by National Natural Science Foundation of China (Grant No. 10871177)Specialized Research Fund for Doctor Program of Higher Education (Grant No. 20060335032)
文摘In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.
基金by the National Social Science Foundation of China(No.20BTJ050).
文摘Consider a two-dimensional renewal risk model,in which the claim sizes{Xk;k≥1}form a sequence of i.i.d.copies of a non-negative random vector whose two components are dependent.Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d.random pairs,with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large.Then a precise large-deviation formula of the aggregate amount of claims is obtained.
