最优投资及最优消费策略

本文假设证券市场为有效竞争均衡市场，在文［１］的基础上，探讨最优投资及最优消费策略，得到最优投资与最优消费决策条件。     

含有随机波动的非线性的最优投资和消费模型

在连续时间模型假设下,研究风险资产价格服从一个带有随机波动的几何布朗运动的最优消费和投资问题．首先建立了最优消费和投资同题随机最优控制数学模型;然后运用随机最优控制理论,得到了最优投资和消费随机最优控制问题的值函数所满足的线性抛物线偏微分方程和非线性抛物线偏微分方程．     

Quasi—uniformities on Lattice Implication Algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｒｄｅｒｔｏｒｅｓｅａｒｃｈｔｈｅｌｏｇｉｃａｌｓｙｓｔｅｍｗｈｏｓｅｐｒｏｐｏｓｉｔｉｏｎａｌｖａｌｕｅｉｓｇｉｖｅｎｉｎａｌａｔｔｉｃｅ，ＸｕＹ．［Ｘｕ２］ｐｒｏｐｏｓｅｄｔｈｅｃｏｎｃｅｐｔｏｆｌａｔｔｉｃｅｉｍｐｌｉｃａｔｉｏｎａｌｇｅｂｒａａｎｄｄｉｓｃｕｓｓｅｄｉｔｓｓｏｍｅｐｒｏｐｅｒ－ｔｉｅｓｉｎ［Ｘｕ１］ａｎｄ［Ｘｕ２］．Ａｌｓｏ，ｉｎ［ＸＱ１］，ＸｕＹ．ｔｏｇｅｔｈｅｒｗｉｔｈＫ．Ｙ．Ｑｉｎｄｉｓｃｕｓｓｅｄｔｈｅｐｒｏｐ－ｅｒｔｉｅｓｏ…     

可压缩格子Boltzmann模型的启示性稳定理论

１引言格子Ｂｏｌｔｚｍａｎｎ方法（ＬＢＭ）是近几年发展起来的一种模拟复杂系统的新方法［１］［２］［３］这种方法已经在流体力学各领域得到应用．最近,许多研究工作集中于用ＬＢＭ模型计算可压缩流体流动．Ａｌｅｘａｎｄｅｒ和Ｃｈｅｎ等［４］提出了可以计算激波的等温模型,模型中的音速是可以选择的．Ｑｉａｎ和Ｏｒｓｚａｇ［５］分析了ＬＢＧＫ模型在可压缩区域内的非线性偏差,给出了激波结构的ＬＢＭ结果．Ｑｉａｎ和Ｏｒｓｚａｇ［６］也计算了弱可压缩的高Ｒｅ数问题,并用于计算Ｋｏｌ－ｍｏｇｏｒｏｖ流．Ａｎｃｏｎａ［…     

血生成模型的全局吸引性

在本文中，我们进一步研究时滞微分方程它由Ｍａｃｋｅｙ和Ｌａｄａｓ［２］提出作为血生成模型．我们建立了（＊）的平衡是全局吸引子的新的充分条件，我们还改进了Ｇｏｐａｌｓａｍｙ，Ｋｕｌｅｎｏｖｉｃ和Ｌａｄａｓ［１］所得到的某些结果．     

积分算子的n-逼近数

本文研究了积分算子ＴＫ：Ｌｑ［０，１］→Ｌｑ［０，１］，（ｑ≥１）当核 Ｋ（ｓ， ｔ）是 Ｓｏｂｏｌｅｖ空间 Ｗｐｒ（［０， １］２）中元素时ｎ－逼近数 ａｎ（ＴＫ： Ｌｑ→ Ｌｑ）的估计，并把这个估计应用于退化核方法解第二类线性Ｆｒｅｄｈｏｌｍ方程（Ｉ一ＴＫ）ｘ＝ｙ时，Ｂａｄｈｖａｌｏｖ［５］意义下最佳误差的讨论中，所得到的最佳误差之估计当ｑ＝１时，最优化了［１０］的结论．     

Minimum Ellipsiod and Optim alDesign

§０．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ［１］，ＫｉｅｆｅｒａｎｄＷｏｌｆｏｗｉｔｚｓｏｌｖｅｄｔｈｅｅｑｕｉｖａｌｅｎｃｅｏｆＧ－ｏｐｔｉｍａｌｄｅｓｉｇｎａｎｄＤ－ｏｐｔｉｍａｌｄｅｓｉｇｎ．Ｉｎｔｈｅｐａｐｅｒ［２］，ＫａｉｌｉｎａｎｄＳｔｕｄｄｅｎｓｔｕｄｉｅｄｔｈｅａｌｇｅｂｒａｉｃｓｔｒｕｃｔｕｏｅｏｆｃｏｎｃｅｓ－ｓｉｏｎａｌｄｅｓｉｇｎ，Ｄ－ｏｐｔｉｍａｌａｎｄＣ－ｏｐｔｉｍａｌｄｅｓｉｇｎ．Ｉｎｔｈｅｐａｐｅｒ［３］，ＳｐｒｕｉｌｌｓｔｕｄｉｅｄｔｈｅＣ－ｏｐｔｉｍ…     

相依序列加权和的收敛性

本文在相依序列下考虑加权和的ａ．ｓ．收敛性和完全收敛性．所得结论推广并改进了［１］、［２］中有关结论．     

Kloosterman和的角度

有限域 Ｆｑ（ｑ为奇）上的 Ｋｌｏｏｓｔｅｒｍａｎ和是两个模为 ｑ１／２的共轭复数之和．这个复数的角度就称为相应的Ｋｌｏｏｓｔｅｒｍａｎ和的角度．我们在本文给出了Ｋｌｏｏｓｔｅｒｍａｎ和的角度的一些结果,改进了Ｋａｔｚ Ｎ．［１］的一些结果,也改进和推广了Ｃｏｎｒｅｙ　Ｊ．和Ｉｗａｎｉｅ Ｈ．［２］的结果．     

Koch曲线的Hausdorff测度的估计

文［１］研究了Ｋｏｃｈ 曲线的Ｈａｕｓｄｏｒｆｆ测度,得到了一个改进了的上限,本文将进一步改进此上限． 有关的予备知识和结论可在［１］中见到．     

New stochastic model for dispersion in heterogeneous porous media: 1. Application to unbounded domains

A new model of solute dispersion in porous media that avoids Fickian assumptions and that can be applied to variable drift velocities as in non-homogeneous or geometrically constricted aquifers, is presented. A key feature is the recognition that because drift velocity acts as a driving coefficient in the kinematical equation that describes random fluid displacements at the pore scale, the use of Ito calculus and related tools from stochastic differential equation theory (SPDE) is required to properly model interaction between pore scale randomness and macroscopic change of the drift velocity. Solute transport is described by formulating an integral version of the solute mass conservation equations, using a probability density. By appropriate linking of this to the related but distinct probability density arising from the kinematical SPDE, it is shown that the evolution of a Gaussian solute plume can be calculated, and in particular its time-dependent variance and hence dispersivity. Exact analytical solutions of the differential and integral equations that this procedure involves, are presented for the case of a constant drift velocity, as well as for a constant velocity gradient. In the former case, diffusive dispersion as familiar from the advection–dispersion equation is recovered. However, in the latter case, it is shown that there are not only reversible kinematical dispersion effects, but also irreversible, intrinsically stochastic contributions in excess of that predicted by diffusive dispersion. Moreover, this intrinsic contribution has a non-linear time dependence and hence opens up the way for an explanation of the strong observed scale dependence of dispersivity.     

Homogenization of a stochastically forced Hamilton-Jacobi equation

We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation is deterministic, and, in general, the noise has an enhancement effect, for which we provide a quantitative estimate. As an application, we perform a noise sensitivity analysis for Hamilton-Jacobi equations forced by a noise term with small amplitude, and identify the scaling at which the macroscopic enhancement effect is felt. The results depend on new, probabilistic estimates for the large scale Hölder regularity of the solutions, which are of independent interest.     

Second-order hyperbolic s.p.d.e.'s driven by homogeneous Gaussian noise on a hyperplane

We study a class of hyperbolic stochastic partial differential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions differ. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.

     

Stochastic Partial Differential Equations on Manifolds~II. Nonlinear Filtering

The conditional law of an unobservable component x(t) of a diffusion (x(t),y(t)) given the observations {y(s):s[0,t]} is investigated when x(t) lives on a submanifold of . The existence of the conditional density with respect to a given measure on is shown under fairly general conditions, and the analytical properties of this density are characterized in terms of the Sobolev spaces used in the first part of this series.     

Stabilization of a class of nonlinear composite stochastic systems

This paper deals with the stability for a class of nonlinear composite stochastic systems by feedback laws.Firstly,we give sufficient conditions for the existence of feedback laws which render the equilibrium solution of the stochastic system globally asymptotically stable in probability.Secondly,for stochastic systems of the same type,we prove that there exists a linear feedback law which exponentially stabilizes in mean square the closed–loop stochastic system at its equilibrium.     

政府投资治理污染的随机增长模型

本文设定了两种不同的带有污染的生产函数.在此两种生产函数情形下,利用随机最优化的方法分别分析了由政府投资治理污染的随机增长模型,得到了以下结论:在宏观均衡条件下,增大污染的外部性指标促进经济增长却降低福利;提高政府的环保投资增加福利,但对增长的影响却与污染的外部性指标和污染的负福利效用权数的大小有关.     

Non-compact-valued stochastic control under state constraints

In the present paper, we study a necessary condition under which the solutions of a stochastic differential equation governed by unbounded control processes, remain in an arbitrarily small neighborhood of a given set of constraints. We prove that, in comparison to the classical constrained control problem with bounded control processes, a further assumption on the growth of control processes is needed in order to obtain a necessary and sufficient condition in terms of viscosity solution of the associated Hamilton-Jacobi-Bellman equation. A rather general example illustrates our main result.     

两参数线性积分微分鞅型随机方程解的存在性,轨道唯一性和收敛性

设M和A，B，C分别为R上的两参数连续平方可积鞅和连续可积适应增过程．在系数a，b，ψ，ψ满足合适的条件下，本文证明了两参数随机方程解的存在性、轨道唯一性和收敛性成立．     

Set-valued stochastic intergrals and stochastic inclutions 1

We present the concepts of set - valued stochastic integrals and stochastic inclusions. The main result of the paper deals with a selection property of set - valued stochastic integrals. This property is a fundamental one for stochastic inclusions.     

An algorithm for stochastic programs with first-order dominance constraints induced by linear recourse

We derive a cutting plane decomposition method for stochastic programs with first-order dominance constraints induced by linear recourse models with continuous variables in the second stage.