完全离散二项风险模型下有限时间内的生存概率

本文用分析方法研究了保险公司在完全离散复合二项风险模型下生存到固定时刻n,在n恰好发生第k次赔付,而且在时刻n的盈余为某数x(x≥0）的概率公式,由此得到了有限时间内的生存概率公式。     

跳跃扩散型离散算术平均亚式期权的近似价格公式

在标的资产价格遵循跳跃扩散过程条件下 ,研究没有封闭形式解的离散算术平均亚式期权 ,运用二阶 Edgeworth逼近得到离散算术平均亚式期权的近似价格公式 .     

Banach空间中带Poisson跳的随机种群方程的数值分析

本文研究Banach空间中带Poisson跳的随机种群方程,通过离散使之成为随机微分方程,进而运用显式Euler公式来分析其数值解与解析解的误差.     

关闭—启动型Geom／G／1离散排队及其在ATM网络中的应用

研究带有关闭延迟和启动时间的Geom/G/1离散时间排队,导出了稳态队长、等待时间的分布及其随机分解结果,该模型可用于ATM网络的虚通道分析,给出响应时间、启动率,闲置率等指标公式。     

任意多边形面积公式的推导及其应用

通过对Green公式的离散变形,建立了重积分到曲线积分的公式,用多种方法推导出任意多形的面积公式.     

随机游走和离散的倒向随机微分方程

本文研究了随机游走和离散的倒向随机微分方程。把随机游走到布朗运动的收敛推广到L^2情形；而且根据倒向随机微分方程的理论框架研究了离散的倒向随机微分方程，得到了离散的倒向随机微分方程解的存在唯一性和比较定理，这实际上给出了倒向随机微分方程的一种离散方法，为理论和实际研究提供了方便。     

含参向量随机序列的递推估计的统一处理

本文讨论了含参向量随机序列的递推估计问题,将参数估计问题和系统的状态估计问题统一了起来,给出了统一的递推估计公式,还具体地讨论了状态方程与量测方程中均含有参向量时线性离散时间系统的递推估计问题以及部分状态分量缺初始值的递推估计问题。     

随机利率及保费的离散风险模型中的破产问题

本文研究了利率、保费均为随机变量的两个离散风险模型.利用递推的方法,得到了有限时间内的破产概率和最终破产概率所满足的积分方程,以及盈余首次穿过给定水平时刻的分布的递推公式,从而可以对保险公司各个破产指标得出数值结论.     

基于单重工作休假的离散时间排队稳态分析

详细地分析了一个单重工作休假的离散时间Geom/G/1排队系统.首先,构造二维嵌入马尔可夫链,得到其M/G/1型转移概率矩阵.其次,利用矩阵分析的方法,导出了稳态队长的概率分布,进一步得到稳态队长的随机分解结果和平均队长公式.最后,给出稳态等待时间的随机分解结构及其平均等待时间公式.     

共球有限点集重心的一个性质——“数学问题”第1753题的推广

1 引言及有关定义 <数学通报>2008年第9期刊登的"数学问题"第1753题是: 求证:正四面体各顶点到其外接球的任一切面的距离之和为定值. 问题提供人在解答过程中用到了下面的距离公式[1].     

Contraction behaviour of iteration–discretization based on gradient type projections

There is a wide range of iterative methods in infinite dimensional spaces to treat variational equations or variational inequalities. As a rule, computational handling of problems in infinite dimensional spaces requires some discretization. Any useful discretization of the original problem leads to families of problems over finite dimensional spaces. Thus, two infinite techniques, namely discretization and iteration are embedded into each other. In the present paper, the behaviour of truncated iterative methods is studied, where at each discretization level only a finite number of steps is performed. In our study no accuracy dependent a posteriori stopping criterion is used. From an algorithmic point of view, the considered methods are of iteration–discretization type. The major aim here is to provide the convergence analysis for the introduced abstract iteration–discretization methods. A special emphasis is given on algorithms for the treatment of variational inequalities with strongly monotone operators over fixed point sets of quasi-nonexpansive mappings.     

一类带有铁磁材料参数的非线性涡流问题的A-φ有限元法

针对带有铁磁材料的非线性涡流问题,其非线性性通常体现在磁场强度和磁感应强度的关系上.本文提出了一种全离散的有限元A-φ格式,分别在时间和空间上采用向后欧拉公式以及节点有限元进行离散.首先,在合适的函数空间里给出时间上的半离散格式,通过考察其弱形式建立相应的适定性理论,并证明近似解收敛于弱解.其次,给出全离散格式并讨论其误差估计.最后,给出两个数值算例以验证理论结果.     

General Inhomogeneous Discrete Linear Partial Differential Equations with Constant Coefficients on the Whole Spaces

In this paper we shall introduce new constructions of approximate solutions of general linear partial differential equations with constant coefficients on the whole spaces, and establish fundamental estimates of the solutions depending on the inhomogeneous terms. This will be done by combining general ideas of the Tikhonov regularization and discretization of bounded linear operator equations on reproducing kernel Hilbert spaces. Furthermore, we will provide approximate solutions for the related inverse source problems.     

On a hybrid boundary element method

Summary. In this paper we study a symmetric boundary element method based on a hybrid discretization of the Steklov–Poincaré operator well suited for a symmetric coupling of finite and boundary elements. The representation used involves only single and double layer potentials and does not require the discretization of the hypersingular integral operator as in the symmetric formulation. The stability of the hybrid Galerkin discretization is based on a BBL–like stability condition for the trial spaces. Numerical examples confirm the theoretical results. Received December 15, 1997 / Revised version received December 21, 1998/ Published online November 17, 1999     

A unified framework for the discretization of nonlinear operator equations

A general theory for the discretization of non-linear operator equations is presented. A given operator with certain continuity and compactness properties is approximated by a sequence of operators acting in different spaces, usually finite dimensional. Connection maps, such as restriction and interpolation, relate the spaces. The abstract convergence theory is formulated in terms of metric spaces. Specializations and applications to differential and integral equations involve normed linear spaces. The case with the same setting for the original and approximate problems was treated in [1]. For typical problems, both types of discretization methods are available. They are related by means of the connection maps.     

Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

In this paper, we study the existence-uniqueness and large deviation estimate for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then we apply them to a large class of semilinear stochastic partial differential equations (SPDE), and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Moreover, stochastic Navier-Stokes equations are also investigated.     

Numerical analysis of semilinear stochastic evolution equations in Banach spaces

The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in L^p-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank–Nicholson scheme. In the last section, we give some examples, i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.     

Coorbit Spaces and Banach Frames on Homogeneous Spaces with Applications to the Sphere

This paper is concerned with the construction of generalized Banach frames on homogeneous spaces. The major tool is a unitary group representation which is square integrable modulo a certain subgroup. By means of this representation, generalized coorbit spaces can be defined. Moreover, we can construct a specific reproducing kernel which, after a judicious discretization, gives rise to atomic decompositions for these coorbit spaces. Furthermore, we show that under certain additional conditions our discretization method generates Banach frames. We also discuss nonlinear approximation schemes based on the atomic decomposition. As a classical example, we apply our construction to the problem of analyzing and approximating functions on the spheres.     

On Lp -Theory of stochastic partialdifferential equations of divergence form with continuous coefficients

We develop an L_p -theory of stochastic PDEs of divergence form. Under natural assumptions on the coefficients and the data, we show that the solutions belong to some modified stochastic Sobolev spaces. As a consequence of this result and certain embedding theorem, we also show that the solutions are Holder continuous in space and time a.s. for sufficiently large p     

Weighted Coorbit Spaces and Banach Frames on Homogeneous Spaces

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted L_p-space. Moreover, we show that a judicious discretization of the representation leads to an atomic decomposition and to Banach frames for these coorbit spaces.