广义函数框架下的小波变换及其性质

本文将L^2空间的小波变换推广到广义函数空间上，建立了广义函数框架下的小波变换，证明了广义函数的小波变换及其有关性质，使小波变换这一信号分析的数学工具有了更大的应用范围．     

G框架下的欧式期权定价公式

用G几何布朗运动描述标的资产的价格变动,得到了欧式看涨期权定价的动态公式,并给出了动态复制策略的显示表达.     

A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework

In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by \(G\) -Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related Hamilton–Jacobi–Bellman (HJB) equation in the framework of \(G\) -expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation.     

在广义函数框架下求解偏微分方程的一种方法

本文是在广义函数的框架下,利用广义函数的一些特殊性质,讨论求解偏微分方程的一种方法。     

条件独立性与条件回归独立性

引入随机变量条件独立、强条件回归独立、逐对条件回归独立、连续条件回归独立、邻对条件回归独立、累积条件回归独立诸定义,证明它们之间的等价关系.     

On the Independence of Hartman Sequences

 Given and , we define by setting if and only if , where denotes the fractional part of α, i.e. α is considered as an element of the torus . If the topological boundary of A has Haar measure 0, then is called a Hartman sequence, which is a generalisation of Kronecker and Beatty sequences. In this article we answer a question of Winkler by showing explicitly for which sets , and vectors , we have . The main tool of the proof is Weyl’s theorem on uniform distribution.     

Independence and atoms

We prove that if the range of a probability measure contains an interval , 0$">, then there are infinitely many (nontrivial) independent events in this probability space.

     

Independence in hypergraphs

Suppose an integral function (|A|)q₁ defined on the subsets of edges of a hypergraph (X,u,) satisfies the following two conditions: 1) any set W u such that |A|(|A|) for any AW is matroidally independent; 2) if W is an independent set, then there exists a unique partitionW=T₁+ T₂+...+T_v such that |T ⁱ |=(|T ⁱ |),i1:v, and for any AW, |A|(|A|) there exists a T_i such that AT_i. The form of such a function is found, in terms of parameters of generalized connected components, hypercycles, and hypertrees.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 196–204, 1982.     

On the Independence of Hartman Sequences

 Given and , we define by setting if and only if , where denotes the fractional part of α, i.e. α is considered as an element of the torus . If the topological boundary of A has Haar measure 0, then is called a Hartman sequence, which is a generalisation of Kronecker and Beatty sequences. In this article we answer a question of Winkler by showing explicitly for which sets , and vectors , we have . The main tool of the proof is Weyl’s theorem on uniform distribution. Received 3 November 2000; in final form 24 April 2001     

Measure-Preserving Functions and the Independence Copula

We solve a problem recently proposed by Kolesárová et al. Specifically, we prove that a necessary and sufficient condition for a given copula to be the independence or product copula is for the pair of measure-preserving transformations representing the copula to be independent as random variables.     

On the Roots of Expected Independence Polynomials

The independence polynomial of a (finite) graph is the generating function for the number of independent sets of each cardinality. Assuming that each possible edge of a complete graph of order n is independently operational with probability p, we consider the expected independence polynomial. We show here that for all fixed , the expected independence polynomials of complete graphs have all real, simple roots.     

随机变量独立性的判别方法

归纳总结判别随机变量独立性的方法,并借助实例加以说明.     

Independence of the axiomatic system for MV-algebras

We prove that the well-known axiomatic system of MV-algebras is not independent. The axiom of commutativity can be deleted and the remaining axioms are shown to be independent.     

有关独立性的一个命题

本文指出了一类离散型随机向量，其中ｎ－１个独立、但是ｎ个不独立。