Ruin Probabilities under a Markovian Risk Model

In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)}t≥0 with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability ψ(0) and the bound for the convergence rate of the ruin probability ψ(u) are given by using the generalized renewal technique developed in this paper.Finally, we prove that the ruin probability ψ(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix(qij)i,j∈E such that qm = qml and qi=qi(i 1), 1≤i≤m-1.     

Some path properties of generalized Lévy sheet

Let X(t) be an N parameter generalized Levy sheet taking values in Rd with a lower index a, R={(s,t] =∏i=1N(si,ti)],si相似文献   

Existence,uniqueness, and global attractivity of positive solutions and MLE of the parameters to the logistic equation with random perturbation

This paper discusses a randomized Logistic equation N(t)=(r αB(t))N(t)[1-(N(t)/K)] with an initial value N(0)=N_0,and N_0 is a random variable satisfying 0＜N_0＜K.The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate(MLE)of the parameters of the equation are studied.     

POSITIVE PERIODIC SOLUTION OF AN INTEGRO-DIFFERENTIAL PREDATOR-PREY SYSTEM WITH INFINITE DELAYS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a differential-integral predator-prey system with infinite delaywhere N1(t), N2(t) satisfy N1(t) =φ1(t), N2(t) =φ2(t), φi∈ BC((∞,0],R+φi(0)> 0,i=1,2, ∫0+∞Ki(s)ds = 1, i=1,2,3.     

A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS

In this article, we consider the dynamics of N two-dimensional boson systems interacting through a pair potential N-1Va(xi-xj) where Va(x) = a-2V (x/a). It is well known that the Gross-Pitaevskii (GP) equation is a nonlinear Schrdinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if ut solves the GP equation, then the family of k-particle density matrices {k ut, k ≥ 1} solves the GP hierarchy. Denote by ψN,t the solution to the N-particle Schrdinger equation. Under the assumption that a = N-ε for 0 ε 3/4, we prove that as N →∞ the limit points of the k-particle density matrices of ψN,t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫V (x) dx.     

局部上同调模的Artin性质

In this paper,let (R,m)be a Noetherian local ring,I(?)R an ideal, M and N be two finitely generated modules.Firstly,we study the properties of H_I~t(M),t=f-depth(I,M) and discuss the relationship between the Artinianness of H_I~i(M,N) and the Artinianness of H_I~i(N).Then,we get that H_I~d(M,N)is I-cofinite,if(R,m)is a d-dimensional Gorenstein local ring.     

GLOBAL ATTRACTIVITY IN THE DISCRETE LASOTA-WAZEWSKA MODEL

§ 1　IntroductionConsider the delay difference equationNn 1 -Nn =-μNn pe- r Nn- k,　 n =0 ,1 ,2 ,... (1 )whereμ∈ (0 ,1 ) ,r,p∈ (0 ,∞ ) and k∈N,where N denotes the setofnonnegative integers.Equation(1 ) is a discrete analogue of the delay differential equationd N(t)dt =-μN(t) pe- r N(t-τ) ,　 t≥ 0 ,(2 )which was used firstby Wazewska-Czyzewska and Lasota[1 ] as a model for the survival ofred blood cells in an animal,see also[2 ] .Here N(t) denotes the number of red blood cellsat…     

Besov空间中双参数Volterra型重分数过程的弱逼近

In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes{B_n(s,t)},n∈N defined by B_n(s,t)=∫_0~s ∫_0~tk_(a(s))(s,u)K_(β(t))(t,u)θ_(n(u,v))dudv,here {θ_n(u, v)}n∈N is a family of processes, converging in law to a Brownian sheet as n→∞,based on the well known Donsker's theorem.     

Age-dependent branching processes in random environments

We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R , and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.     

Optimum Super-simple Mixed Covering Arrays of Type a~1b~(k-1)

A mixed covering array(MCA) of type(v_1, v_2,..., v_k), denoted by MCA_λ(N; t, k,(v_1, v_2,..., v_k)), is an N × k array with entries in the i-th column from a set V_i of v_i symbols and has the property that each N × t sub-array covers all the t-tuples at least λ times, where 1 ≤ i ≤ k. An MCA_λ(N; t, k,(v_1, v_2,..., v_k)) is said to be super-simple, if each of its N ×(t + 1) sub-arrays contains each(t + 1)-tuple at most once. Recently, it was proved by Tang, Yin and the author that an optimum super-simple MCA of type(a, b, b,..., b) is equivalent to a mixed detecting array(DTA)of type(a, b, b,..., b) with optimum size. Such DTAs can be used to generate test suites to identify and determine the interaction faults between the factors in a component-based system. In this paper,some combinatorial constructions of optimum super-simple MCAs of type(a, b, b,..., b) are prov_ided.By employing these constructions, some optimum super-simple MCAs are then obtained. In particular, the spectrum across which optimum super-simple MCA_2(2b~2; 2, 4,(a, b, b, b))' s exist, is completely determined, where 2 ≤ a ≤ b.     

中立型对数种群模型的正周期解存在性

本文利用k-集压缩算子的拓朴度抽象连续定理和某些分析技巧,研究了一类中立型对数种群模型dN/dt=N(t)[r(t)-a(t)lnN(t-σ)-b(t)d/dtlnN(t-r)]的正周期解存在性问题。得到了正周期解存在性的新结果。     

非线性中立型时滞方程解的全局渐近稳定性和振动性

本文研究非线性中立型时滞微分方程N( t) =N( t) [a( t) -b( t) N ( t-τ) -c( t) N( t-σ) -d( t) N ( t) ],t≥ t0 ,( E)其中τ,σ∈ [0 ,∞ ) ,a( t) ,b( t) ,d( t)∈ C1( [t0 ,∞ ) ,R+) ,c( t)∈ C( [t0 ,∞ ) ,k) ,得到方程 ( E)的正解关于正常数平衡点全局渐近稳定和振动的充分条件 .本文所用方法与其他文献不同 ,所得结果发展了一些文献的结果 ,其中定理 ( 2 .3)回答了由 Y.Kuang and A.Feldstein所提出的一个公开问题 .     

一类四阶差分方程边值问题Extremal的存在性

本文运用上,下解单调迭代技巧讨论四阶差分方程两点边值问题{△~2(g△~u(t-2)))=f(t,u(t),△~u(t-1)),t∈{2,3…,N},u(0)=u(N+2)=△~u(0)=△~2u(N)=0解的存在性,其中N＞2是一个固定的自然数,f:{2,3,…,N}×R~2→R连续,g:R→R连续,严格单调递增且g(0)=0.     

关于偶数阶中立型微分方程的线性化振动的一个注记

就偶数阶中立型时滞微分方程的所有有界解的振动性而言,研究了偶数阶非 线性中立型时滞微分方程［ｘ（ｔ）－ｐ（ｔ）ｘ（ｔ－τ）］－ｑ（ｔ）ｈ（ｘ（ｔ－σ））＝０和与它相应的 线性方程［ｘ（ｔ）－ｐ_０ｘ（ｔ－τ）］－ｑ-０ｘ（ｔ－τ）＝０在振动性上的等价性．所得结果改进 了 Ｌａｄａｓ Ｇ,和 Ｑｉａｎ Ｃ．的一个结果．     

ON THE EXISTENCE OF NONTRIVIAL PERIODIC SOLUTIONS OF DIFFERENTIAL DIFFERENCE EQUATIONS

This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.     

一类二阶泛函微分方程的多重周期解

利用变分原理和Z_2不变群指标,得出二阶泛函微分方程x″(t-τ)+c(x(t)-x(t-2τ))′-x(t-τ)+λf(t,x(t),x(t-τ),x(t-2τ))=0的多重周期解的存在性质.     

二阶拟线性中立型时滞微分方程的振动性

考虑二阶中立型时滞微分方程[a(t)|(x(t) p(t)x(t-τ)）′|^α-1(x(t) p(t)x(t-τ））′]′ f(t,x(t-σ））=0(E)其中α，τ，σ是非负常数，a(t),p(t)∈C([t0,∞），R），f(t,x)∈C(R,R)。建立了方程（E）的一些新的振动条件。     

完美门限方案的组合构造

部分平衡t-设计t-(v; b;w; 1; 0) (X;A) 称为可划分的, 如果它同时也是一个部分平衡(t-1)-设计(t -1)-(v; b;w; λ_t-1; 0) 并且可将区组集A划分为A₁;…;A_λt-1; 使得每个(X;A_i) (1≤i≤λ_t-1)是一个部分平衡(t-1)-设计(t-1)-(v; b/λ_t-1;w; 1; 0). 本文证明可划分部分平衡t-设计PPBD t-(v; b;w;λ_t-1; 1; 0) 的存在性蕴含着完美(t;w; v;λ_t-1)-门限方案的存在性; 而且在某些情况下, 最优可划分部分平衡t-设计OPPBD(t;w; v) 的存在性等价于最优(t;w; v)-门限方案的存在性. 由此我们得到了最优(t;w; v)-门限方案的一些新的无穷类.     

二阶非线性中立型时滞微分方程的振动准则

文章考虑二阶非线性中立型微分方程a(t)x(t)+∑li=1ci(t)x(t-τi(t))″+∑mi=1pi(t)fi(x(t-δi(t)))-∑ni=1qi(t)gi(x(t-σi(t)))=0的振动性,获得了该方程所有解振动的充分条件,推广了有关文献的结果.     

中立型无穷时滞积分微分方程的周期解与稳定性

考虑了如下中立型周期微分系统ddtx(t)-∫t-∞B(t,s)x(s)ds=A(t,x(t))x(t)+∫t-∞C(t,s)x(s)ds+g(t,x(t-τ))+b(t)的周期解存在性及其稳定性问题,给出其周期解存在的充分条件.