Markov骨架过程积分型泛函的分布和矩及其应用举例

侯振挺等^[1]引入了一类具有广泛应用前景的随机过程－Markov骨架过程,本文研究这类过程积分型泛函的分布和矩及其计算问题,作为应用,我们得到了Doob过程,生灰2过程积分型泛函的分布和矩的公式,尤其对于生灭过程,利用本文的方法也得到了[4]中定理1－3的结果。     

On Variation of Single Birth Processes

Suppose {X（t）; t≥ 0} is a single birth process with birth rate qii＋l （i 〉 0） and death rate qij （i 〉 j ≥ 0）. It is proved in this paper that （i） if there exists aconstant c≥ 0 such that b（i）-a（i）＋ci is nondecreasing with respect to i and a（i） ＋ u（i） - ci ≥ 0 （i≥ 0）, then VarX（t）-EX（t）≥-X（0）e^-2ct,t≥0, or （ii） if there exists a constant u（i） - c≥ 0 such that b（i）-a（i）＋ci is non-increasing with respect to i and a（i）＋u（i）-ci≤0（i≥0）,then VarX（t） - EX（t） ≤ -X（0）e^-2c,t ≥ 0 Hereb（i） = qii＋1, a（0） = 0, a（i） = ∑j=^ijqii-j （i≥ 1）, u（0） = u（1） =0 and u（i） = 1/2∑j=^ij（j - 1）qii-j （i ≥ 2） . This result covers the results for birth-death processes obtained in [7].     

Hessians of the Calabi Functional and the Norm Function

We first present a new proof of a result of Calabi, nonnegativeness of the Hessian of the Calabi functional at an extremal Kähler metric. Then we extend the result to the general context of a reductive group action on a Kähler manifold admitting a moment map. Precisely, we show nonnegativeness of the Hessian of the norm function along a complex orbit at a critical point. Mathematics Subject Classification (1991): Primary 53C55; Secondary 53D20, 58E11     

生灭型半马氏骨架过程

本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τn-1(ω)与τn(ω)之间的嵌入过程X(n)(t,ω)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布.     

Probability Inequalities and Limit Theorems for Generalized L-Statistics

We obtain exponential upper bounds for tails of distributions of generalized L-statistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized L-statistics based on a sample from the uniform distribution on [0,1] and of L-statistics with decomposed kernels (without any restrictions on the sample distribution type).     

Some Cubic Birth and Death Processes and their Related Orthogonal Polynomials

The orthogonal polynomials with recurrence relation (λ,_n +μ_n-z)F_n(z) = μ_n+1F_n+1(z)+λ_n-1F_n-1(z) with two kinds of cubic transition rates λ_n and μ_n, corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes of polynomials, which enable us to compute their Nevanlinna matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex plane.     

Products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces

Siberian Mathematical Journal - We give a complete picture of the boundedness and compactness of the products of integral-type operators and composition operators from the mixed norm space to...     

比较原理和带马尔可夫调制的随机泛函微分方程

本文考虑带马尔可夫调制的随机泛函微分方程解的不稳定性,通过建立的新的比较原理,得到一些不稳定的判据.     

Inverse Theorem of Approximation in L_p for the Stancu Integral-type Operators on a Simplex

In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in Lp(1≤p< ∞)has been obtained.     

Markov process functionals in finance and insurance

The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.     

SINGLE BIRTH PROCESSES

1.IntroductionLetusstartfromthetime-continuouscase.Then,theQ-matrixofasinglebirthprocessisasfollows:Throughoutthenote,weconsideronlytotallystableandconservativeQ-matrix:forallDuetothefactthattheboundaryofsuchQ-matrixisatmostsingleexit,thesinglebirthp...     

线性过程关于矩的重对数律的精确率

讨论线性过程Xk=∑∞i=-∞ai+kεi,其中{εi;-∞＜i＜∞}是均值为零,方差有限为σ2的双侧无穷独立同分布随机变量序列,{ai;-∞＜ i＜∞}为绝对可和的实数序列.令Sn=∑nl=1Xk,n≥1,假设|ε1|3＜∞,证明了对任意的δ＞-1,lim ∈↘0∈2δ+2∑∞n=1(㏒ ㏒ n)δ/n3/2㏒ nE{|Sn|-∈τ√2n ㏒ ㏒ n}+=√2τ√/√π(δ+1)(2δ+3)Γ(δ+2),其中τ2=σ2(∑∞i=-∞ai)2以及Γ(·)为Gamma函数.     

Thinning of point processes,revisited

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Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras

We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.