修改的Poisson核和调和函数的积分表示

在本文中,对于半平面中的调和函数u(z),利用半平面中修改的Poisson核,证明了如果它的正部u~ (z)=max{u(z),0}满足某些限制增长条件,则它可以用半平面边界上的积分表示出来,并且它的负部u~-(z)=max{-u(z),0}也被类似的增长条件所控制,这一结果改进了在半平面中调和函数的某些经典结果。     

球面上的Poisson积分

证明了球面上的Poisson积分算子从Lp(Sn?1)到Lorentz空间Lq,1(B1)(q 1)有界,且从有界Borel测度集M(Sn?1)到Lq,1(B1)(q < nn?1)有界,推广了部分已知的结果.进一步构造了一个反例说明了球面上的Poisson积分算子不一定从M(Sn?1)到L n n?1(B1)有界.     

多重Poisson积分的乘积公式

本文在Poisson白噪声空间中讨论了多重Poisson积分的乘积,在一定条件下,给出了具体的乘积公式。     

向量随机测度关于白噪声的积分的收敛性

本文主要讨论s.i.s.向量随机测度关于白噪声的积分的收敛性,我们得到了如下结果设X是具type2的Banach空间,{Fn}∞n=0是一列被μ所控制的X值s.i.s随机测度,对任意的E∈∑,E[Fn(E)]=0,E‖Fn(E)‖2＜+∞,{Fn(E)}∞n=0是一致W弱可积,且{Fn}∞n=1弱几乎收敛到F0,则(1)对每个n≥0∫FndW是s.i.s向量随机测度;(2)∫FndWwp→∫F0dW.     

一类重随机Poisson过程在信用风险定价模型中的应用

运用带随机尺度因子的重随机Poisson过程描述信用衍生产品的违约可能，在违约强度λ(t)是随机变量的情况下得到违约时间τ的分布密度函数，并推导出信用衍生产品的定价模型．     

关于白噪声的L_2－泛函在Malliavin算子作用下的积分表示

本文基于非线性空间的张量积结构，建立了抽象可测空间（ＴＳＦＨＢ，）上关于白噪声测度Ｘ的（非适应）随机积分．应用Ｃｈａｏｓ分解，得出了关于白噪声的一般Ｌ２－泛函ξ的如下积分表示式　进一步，我们讨论了所建立的随机积分在Ｍａｌｌｉａｎ算子Ｌ作用下的特点，从而获得ξ在Ｌ作用下的如下随机积分表示     

关于白噪声的L2—泛函在Malliavin算子作用下的积分表示

本文基于非线性空间的张量积结构，建立了抽象可测空间上关于白噪声测度Ｘ的随机积分。     

Mbius变换和正则函数的Poisson积分表示

首先,给出了R³中平面和球面方程的超复形式,接着提出了R3中平面和球面方程的超复形式,接着提出了R³中关于平面和球面对称点的概念,并给出了关于平面和球面对称点所满足的等价方程.我们考虑了超复空间Cl_3中的一些特殊的Mbius变换,并给出了其一些性质,比如:保持球面或平面不变性,保持关于平面和球面对称性不变性,保持交比不变性等.文中给出了正则函数和Mbius变换的关系.其次,证明了R3中关于平面和球面对称点的概念,并给出了关于平面和球面对称点所满足的等价方程.我们考虑了超复空间Cl_3中的一些特殊的Mbius变换,并给出了其一些性质,比如:保持球面或平面不变性,保持关于平面和球面对称性不变性,保持交比不变性等.文中给出了正则函数和Mbius变换的关系.其次,证明了R³中球内正则函数的推广的Cauchy定理和Cauchy积分公式.借助于上述正则函数的Cauchy积分公式和其对称点的积分表示,给出了正则函数的Poisson积分表示.最后,在Mbius变换的性质基础上,给出了Mbius变换下曲面积分的变量替换公式.     

带Poisson 跳跃的正倒向随机延迟系统递归最优控制问题的最大值原理

本文研究了带Poisson 跳跃的正倒向随机延迟系统的递归最优控制问题. 利用经典的针状变分方法、对偶技术和带Poisson 跳跃的超前倒向随机微分方程的相关结果, 证明了最优控制的最大值原理, 包括了最优控制满足的必要条件和充分条件.     

A white noise approach to infinitely divisible distributions on Gel'fand triple

In this note, we apply white noise analysis to infinitely divisible distributions on a real Gel'fand triple E⊂H⊂E^∗. We first introduce an index, called Hida index, for a measure on E⊂H⊂E^∗. And then, under some mild conditions, we obtain a general inequality which indicates a connection between the Hida index of an infinitely divisible distribution on E⊂H⊂E^∗ and that of its Lévy measure. Finally we prove that the Hida index of the standard compound Poisson distribution on E⊂H⊂E^∗ is exactly 1.     

Additive Kernels and Integral Representation of Potentials

Let P=(P _t ) _t>0 be a submarkovian semigroup of kernels on a measurable space (X,). An additive kernel of P is a kernel K from X into ]0,[ such that P _t K(x,A)=K(x,A+t) for every t>0,xX and every Borel subset A of ]0,[. It is proved in this paper that for every potential f of P, there exits an additive kernel K of P, unique (up to equivalence) such that f=K1=₀ K(,dt). This result is already well known for regular potentials of right processes. If U=(U _p ) _p>0 is a sub-Markovian resolvent of kernels on (X,), we give a notion of additive kernel of U and we prove a similar integral representation of potentials of U.     

Continuity and Boundedness of Infinitely Divisible Processes: A Poisson Point Process Approach

Sufficient conditions for boundedness and continuity are obtained for stochastically continuous infinitely divisible processes, without Gaussian component, {Y(t),t T}, where T is a compact metric space or pseudo-metric space. Such processes have a version given by Y(t)=X(t)+b(t),tT where b is a deterministic drift function and

A Radial Derivative with Boundary Values of the Spherical Poisson Integral

A formula of a radial derivative is obtained with the aid of derivatives with respect to and to of the functions closely connected with the spherical Poisson integral and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates .     

Representation of the Stieltjes Integral in Terms of the Riemann Integral Depending on a Parameter

In this paper, we obtain a new formula for the representation of the Riemann-Stieltjes integral of a continuous function in terms of the passage to the limit with respect to the parameter in a Riemann integral depending on this parameter. The derivation of this formula is based on the study of the functional properties of the solution of the auxiliary difference equation of first order representing the weighted first difference of a given function in the form of a simple first difference of an unknown function. The result obtained can be used for the analytic and approximate calculation of Stieltjes integrals.     

半平面中调和函数的积分表示

In this article, we consider the integral representation of harmonic functions. Using a property of the modified Poisson kernel in a half plane, we prove that a harmonic function u（z） in a half plane with its positive part u^＋（z） = max{u（z）, 0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.     

Stochastic Convexity of the Poisson Mixture Model

This paper is devoted to the study of the compound Poisson mixture model in an actuarial framework. Using the s-convex stochastic orderings and stochastic s-convexity, several problems involving an unknown mixing parameter with given moments are examined; namely, the specification of the number of support points in a finite mixture model, and the derivation of extremal mixture distributions. The theory is enhanced with the derivation of theoretical and numerical bounds on several quantities of actuarial interest.     

复合泊松过程的可加性

对复合泊松分布可加性的研究在许多的文献中都可以看到,本文首先应用特征函数的方法证明了复合泊松分布的可加性.以此为基础,结合对随机过程相关性质的讨论,证明了复合泊松过程也具有与复合泊松分布可加性相似的,某种意义上的可加性性质.