THE FUBINI THEOREMS OF STOCHASTIC MEASURES

This paper discusses the existence of product measures of two specific kinds of stoehastic measures,and expands the integrable classes from classes of real measurable functions to ones which consist of some Banach space valued mappings.With the help of this newly defined stochastie integral, which is called S.B.integral,we have proved three Fubini Theorems:Theorem 1.7,Theorem 1.8 and Theorem 2.7.     

POSITIVENESS THEOREMS OF SOLUTIONS FOR SEVERAL DIFFERENTIAL INEQUALITIES AND THEIR APPLICATIONS

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REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained,The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

STRONG LIMIT THEOREMS FOR BLOCKWISE m-DEPENDENT RANDOM VARIABLES AND A GENERALIZATION OF THE CONJECTURES OF MORICZ

The authors introduce the definition of block-wise m-dependent with respect to somepositive real sequence for random variables taking values in a separable Banach space,prove some general results on the strong convergence of blockwise m-dependent randomvariables,and in particular,give positive answers to Móricz conjectures([5])by asharper theorem.     

SMOOTH POINT MEASURES AND DIFFEOMORPHISM GROUPS

Let X=R~d(d>1).Consider the unitary representations of Diff(X)given by quasi-invariant measures under the action of Diff(X).The author proposes smooth point measuresas generalization of Poisson point measures and proves that every smooth point measure isquasi-invariant under the action of Diff(X)and if {U_g~i},i=1,2,are the unitary represen-tations of Diff(X)given by the smooth point measures μ_i,i=1,2,respectively,then {U_g~1}is unitarily equivalent to {U_g~2} iff μ_1 is equivalent to μ_2 as measure.     

ON CONJUGATE QUASI-FOURIER-LEGENDRE-SERIES AND EQUICONVERGENCE THEOREMS

In this paper,we discuss the“conjugate”Quasi-Fourier-Legendre(Q.F.L.)series andthe corresponding conjugate function.Moreover we give some equiconvergence theorems andapplications.     

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

This paper obtains functional modulus of continuity and Strassen's functional LIL of the infinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exact modulus of continuity and LIL of this process respectively.     

A GENERALIZATION OF HIRSCH′S THEOREMS

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H-SEPARABLE RINGS AND THEIR HOPF-GALOIS EXTENSIONS

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WEYL＇S TYPE THEOREMS AND HYPERCYCLIC OPERATORS

For a bounded operator T acting on an infinite dimensional separable Hilbert space H,we prove the following assertions: (i) If T or T* ∈ SC,then generalized aBrowder's theorem holds for f(T) for every ...     

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in Rd, (0<α<2), whose branching rate function is dt, and branching mechanism is of the form ■(z) = z1 β(0 <β≤1). Let Xr and Yr denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xτ and Yτ are discussed.     

PERTURBATION THEOREMS ON HERMITIAN MATRICES AND NEARLY HERMITIAN MATRICES

The problem of relating the eigervalues of an n×n Hermitian matrix to those of its Rayleigh-Ritz approximation is considered. The same residual bound for unitarily invariant norms on Hermilian matrices is obtained even without the orlhonormal and Rayleigh-Ritz assumptions in Stewart and Sun's book [9,Theorem IV. 4.14]. The result can also be extended to nearly Hermitian matrices.     

EXISTENCE AND UNIQUENESS THEOREMS FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS

An existence and uniqueness of solutions for boundary value problemsandare established, by employing a priori estimates for all solutions and the Schau-der fixed point theorem. Some of these results extend earlier results due toUsmani(1979), Yang(1988), and Pei(1997).     

CANONICAL CORRELATION EQUATIONS AND THEIR EXTREMAL PROPERTIES

The canonical variables and canonical correlation coefficients satisfy a matrix equation which is called the canonical correlation equation. There are some different forms of the canonical correlation e-quations given in the literature. In this paper, we discuss four different forms of the canonical correlation equations. The purpose of this paper is to give extremal properties of the solutions of the canonical correlation equations. The results show that canonical variables maximize the determinant of the dispersion matrix of the transformed variables.     

THE WEAK PROJECTION THEORY AND DECOMPOSITIONS OF QUASIMARTINGALE MEASURES

In this paper it is proved that every bounded,×-measurable function has a uniquepredictable projection and that every admissible measure has a unique dual predictableprojection.Using this weak projection theory,the author proves a weak version of Doob-Meyer's decomposition theorem for regular quasi-martingale measures.     

M-BAYESIAN CREDIBLE LIMIT METHOD OF PARAMETER AND ITS APPLICATION

This article develops a new method, named M-Bayesian credible limit method, to estimate reliability parameter. In the article, the M-Bayesian credible limit method of failure rate is derived for zero-failure data from products with exponential distribution. Relations between M-Bayesian credible limit and other classical confidence limits are discussed. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.     

SOME NEW RESULTS ON MARTINGALE INEQUALITIES AND GEOMETRY IN BANACH SPACES

Here we shall state some new results in Banach-space-valued martingale theory and the geometry of Banach spaces which have been obtained since 1986. The topics covered include investigations on nine parts: (1) A basic theorem, (2) Good λ-inequalities, (3) Φ-inequalities, (4) Local convergence, (5) BMO and bounded-     

ON RANDOM TOPOLOGICAL DEGREE AND SOME RANDOM FIXED POINT THEOREMS

In this paper we first introduce random topological degree, and then we use random topological degree to prove some new random fixed point theorems which are the randomization of the wellknown classical theorems of AItman and Krasnosalskii etc. We also proved some other new random fixed point theorems. We first introduce topological degree method to random fixed posnt theory.     

FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES

Results regarding best approximation and best Simultaneous approximation on convexmetric spaces are Obtained.Existence of fixed points for an ultimately nonexpansivesemigroup of mappings is also shown.