This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts servi...This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.展开更多
Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.展开更多
This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectiv...This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.展开更多
This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-se...This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.展开更多
In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u + v^P(x0, t) - au^τ, x ∈ Ω, t 〉 0, △u + v^P(x0, t...In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u + v^P(x0, t) - au^τ, x ∈ Ω, t 〉 0, △u + v^P(x0, t) - bu^τ, x ∈ Ω, t 〉 0 subject to homogeneous Dirichlet conditions and nonnegative initial data, where x0 ∈ Ω is a fixed point, p, q, r, s ≥ 1 and a, b 〉 0 are constants. In the situation when nonnegative solution (u, v) of the above problem blows up in finite time, it is showed that the blow-up is global and this differs from the local sources case. Moreover, for the special case r = s = 1, lim t→T*(T*-t)^p+1/pq-1u(x,t)=(p+1)^1/pq-1(q+1)^p/pq-1(pq-1)^-p+1/pq-1, lim t→T*(T*-t)^q+1/pq-1u(x,t)=(p+1)^1/pq-1(q+1)^p/pq-1(pq-1)^-p+1/pq-1 are obtained uniformly on compact subsets of/2, where T* is the blow-up time.展开更多
In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating acco...In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.展开更多
In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property k,k=Ⅰ, Ⅱ,Ⅲ, and discuss the relationship between the locally asymptotic-norming property and t...In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property k,k=Ⅰ, Ⅱ,Ⅲ, and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.展开更多
We define the topological tail pressure and the conditional pressure for asymptotically sub-additive continuous potentials on topological dynamical systems and obtain a variational principle for the topological tail p...We define the topological tail pressure and the conditional pressure for asymptotically sub-additive continuous potentials on topological dynamical systems and obtain a variational principle for the topological tail pressure without any additional assumptions.展开更多
Let X,X1,X2 be i. i. d. random variables with EX^2+δ〈∞ (for some δ〉0). Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ* (n)=supx∈zζ(x,n),ζ(x,n) =#{0≤k≤n:[Sk]=x}. A s...Let X,X1,X2 be i. i. d. random variables with EX^2+δ〈∞ (for some δ〉0). Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ* (n)=supx∈zζ(x,n),ζ(x,n) =#{0≤k≤n:[Sk]=x}. A strong approximation of ζ(n) by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ*(n) are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ*(n) is proved.展开更多
In this paper, the problem of locally optimum detection of weak pulse signals in narrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimum detectors (LOD) and the corresponding p...In this paper, the problem of locally optimum detection of weak pulse signals in narrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimum detectors (LOD) and the corresponding physical meaning is explained. On the basis of this generalized model, the LOD structures are derived for detecting both coherent- and incoherent-pulse signals in narrow-band non-Gaussian noise. The asymptotic relative efficiency (ARE) due to Pitman is used to evaluate the performance of these LODs. Finally, numerical calculations are carried out for the AREs of these LODs and some valuable results are obtained.展开更多
We study the convergence and asymptotic compatibility of higher order collocation methods for nonlocal operators inspired by peridynamics,a nonlocal formulation of continuum mechanics.We prove that the methods are opt...We study the convergence and asymptotic compatibility of higher order collocation methods for nonlocal operators inspired by peridynamics,a nonlocal formulation of continuum mechanics.We prove that the methods are optimally convergent with respect to the polynomial degree of the approximation.A numerical method is said to be asymptotically compatible if the sequence of approximate solutions of the nonlocal problem converges to the solution of the corresponding local problem as the horizon and the grid sizes simultaneously approach zero.We carry out a calibration process via Taylor series expansions and a scaling of the nonlocal operator via a strain energy density argument to ensure that the resulting collocation methods are asymptotically compatible.We fnd that,for polynomial degrees greater than or equal to two,there exists a calibration constant independent of the horizon size and the grid size such that the resulting collocation methods for the nonlocal difusion are asymptotically compatible.We verify these fndings through extensive numerical experiments.展开更多
The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X ...The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X is Frechét differentiable if and only if X has B(X)-ANP-I, X is quasi-Frechét differentiable if and only if X has B(X)-ANP-II and X is very smooth if and only if X has B(X)-ANP-II′. A new local asymptotic-norming property is also introduced, and the relationship among this one and other local asymptotic-norming properties and some topological properties is discussed. In addition, this paper gives a negative answer to the open question raised by Hu and Lin in Bull. Austral. Math. Soc,45,1992.展开更多
文摘This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(Grant No.20YJA910006)Natural Science Foundation of Jiangsu Province of China(Grant No.BK20201396)+2 种基金supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX211939)supported by the Research Grants Council of Hong KongChina(Grant No.HKU17329216)。
文摘This paper studies the joint tail behavior of two randomly weighted sums∑_(i=1)^(m)Θ_(i)X_(i)and∑_(j=1)^(n)θ_(j)Y_(j)for some m,n∈N∪{∞},in which the primary random variables{X_(i);i∈N}and{Y_(i);i∈N},respectively,are real-valued,dependent and heavy-tailed,while the random weights{Θi,θi;i∈N}are nonnegative and arbitrarily dependent,but the three sequences{X_(i);i∈N},{Y_(i);i∈N}and{Θ_(i),θ_(i);i∈N}are mutually independent.Under two types of weak dependence assumptions on the heavy-tailed primary random variables and some mild moment conditions on the random weights,we establish some(uniformly)asymptotic formulas for the joint tail probability of the two randomly weighted sums,expressing the insensitivity with respect to the underlying weak dependence structures.As applications,we consider both discrete-time and continuous-time insurance risk models,and obtain some asymptotic results for ruin probabilities.
基金the National Natural Science Foundation of China,and the Natural Science Foundation of Shanxi Province and the Youth Scientific
文摘This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.
基金This study is supported partially by the research program of natural science of universities in Jiangsu province(05KJB110144 and 05KJB110063)the natural science foundation of Yancheng normal institute.
文摘In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u + v^P(x0, t) - au^τ, x ∈ Ω, t 〉 0, △u + v^P(x0, t) - bu^τ, x ∈ Ω, t 〉 0 subject to homogeneous Dirichlet conditions and nonnegative initial data, where x0 ∈ Ω is a fixed point, p, q, r, s ≥ 1 and a, b 〉 0 are constants. In the situation when nonnegative solution (u, v) of the above problem blows up in finite time, it is showed that the blow-up is global and this differs from the local sources case. Moreover, for the special case r = s = 1, lim t→T*(T*-t)^p+1/pq-1u(x,t)=(p+1)^1/pq-1(q+1)^p/pq-1(pq-1)^-p+1/pq-1, lim t→T*(T*-t)^q+1/pq-1u(x,t)=(p+1)^1/pq-1(q+1)^p/pq-1(pq-1)^-p+1/pq-1 are obtained uniformly on compact subsets of/2, where T* is the blow-up time.
基金supported by the National Natural Science Foundation of China(11101451)Ph.D.Programs Foundation of Ministry of Education of China(20110191110033)
文摘In the present paper, we consider a kind of semi-Markov risk model (SMRM) with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.
文摘In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property k,k=Ⅰ, Ⅱ,Ⅲ, and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
基金The NSF(11471114,11671208,11431012 and 11271191)of Chinathe National Basic Research Program(2013CB834100)of China(973 Program)
文摘We define the topological tail pressure and the conditional pressure for asymptotically sub-additive continuous potentials on topological dynamical systems and obtain a variational principle for the topological tail pressure without any additional assumptions.
文摘Let X,X1,X2 be i. i. d. random variables with EX^2+δ〈∞ (for some δ〉0). Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ* (n)=supx∈zζ(x,n),ζ(x,n) =#{0≤k≤n:[Sk]=x}. A strong approximation of ζ(n) by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ*(n) are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ*(n) is proved.
文摘In this paper, the problem of locally optimum detection of weak pulse signals in narrow-band non-Gaussian noise is discussed. A generalized model is proposed for locally optimum detectors (LOD) and the corresponding physical meaning is explained. On the basis of this generalized model, the LOD structures are derived for detecting both coherent- and incoherent-pulse signals in narrow-band non-Gaussian noise. The asymptotic relative efficiency (ARE) due to Pitman is used to evaluate the performance of these LODs. Finally, numerical calculations are carried out for the AREs of these LODs and some valuable results are obtained.
文摘We study the convergence and asymptotic compatibility of higher order collocation methods for nonlocal operators inspired by peridynamics,a nonlocal formulation of continuum mechanics.We prove that the methods are optimally convergent with respect to the polynomial degree of the approximation.A numerical method is said to be asymptotically compatible if the sequence of approximate solutions of the nonlocal problem converges to the solution of the corresponding local problem as the horizon and the grid sizes simultaneously approach zero.We carry out a calibration process via Taylor series expansions and a scaling of the nonlocal operator via a strain energy density argument to ensure that the resulting collocation methods are asymptotically compatible.We fnd that,for polynomial degrees greater than or equal to two,there exists a calibration constant independent of the horizon size and the grid size such that the resulting collocation methods for the nonlocal difusion are asymptotically compatible.We verify these fndings through extensive numerical experiments.
基金National Natural Science Foundation of China(10671118) the Natural Science Foundation of Shanghai Education Committee (06NZ016)
文摘The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X is Frechét differentiable if and only if X has B(X)-ANP-I, X is quasi-Frechét differentiable if and only if X has B(X)-ANP-II and X is very smooth if and only if X has B(X)-ANP-II′. A new local asymptotic-norming property is also introduced, and the relationship among this one and other local asymptotic-norming properties and some topological properties is discussed. In addition, this paper gives a negative answer to the open question raised by Hu and Lin in Bull. Austral. Math. Soc,45,1992.