条件期望的两种定义及其等价性探讨

讨论随机变最在给定子σ代数下条件期望的定义,利用投影定理这一数学工具给出条件期望的几何定义,并通过对它与现今各种概率论基础或随机过程教材中常见的公理化定义相互等价性的证明,揭示了条件期望这一概念的内涵.     

下模(上模)不可加测度的条件期望(英文)

本文研究了下模(上模)不可加测度的条件期望.利用下模不可加测度μ的Choquet积分的最大可加表示定理定义了下模(上模)不可加测度的条件期望, 并且证明了这种条件期望的相关性质.     

多元随机序列泛函的强偏差定理

利用熵密度和样本偏差率的概念,建立了多元随机序列泛函关于条件期望的用不等式表示的强极限性质(称之为强偏差定理),在推论部分得到了非齐次马氏链的强偏差定理和随机条件概率的调和平均值的极限性质等相关结论.证明中给出了将条件矩母函数应用于研究多元随机序列泛函的强极限性质的一种途径.     

具有随机控制函数的受控分枝过程

本文研究了具有随机控制函数的受控分枝过程的各类概率母函数间的关系.利用对概率母函数求导的方法,获得了过程的期望和方差,推广了该过程概率母函数和矩量的一些基本结果.     

Completely positive projections on a Hilbert space

The purpose of this paper is to prove that a completely positive projection on a Hilbert space associated with a standard form of a von Neumann algebra induces the existence of a conditional expectation of the von Neumann algebra with respect to a normal state, and we consider the application to a standard form of an injective von Neumann algebra.

     

关于条件期望的注记

利用条件期望的定义和性质给出了两个例子说明随机变量序列的条件期望唯一存在的情况.     

Conditional expectation and the Bergman projection

For any σ-algebra of measurable subsets of the unit disk generated by a finite Blaschke product, we prove that the associated conditional expectation operator commutes with the Bergman projection operator if and only if the σ-algebra is generated by a monomial. In the process, a formula for the conditional expectation operator (under certain assumptions) is obtained. When compared with earlier results of A.B. Aleksandrov concerning conditional expectation associated with σ-algebras of measurable subsets of the circle, our results exhibit a stark contrast between the way conditional expectation operators act in the Bergman and Hardy space settings.     

An Andô-Douglas type theorem in Riesz spaces with a conditional expectation

In this paper we formulate and prove analogues of the Hahn-Jordan decomposition and an Andô-Douglas-Radon-Nikodým theorem in Dedekind complete Riesz spaces with a weak order unit, in the presence of a Riesz space conditional expectation operator. As a consequence we can characterize those subspaces of the Riesz space which are ranges of conditional expectation operators commuting with the given conditional expectation operators and which have a larger range space. This provides the first step towards a formulation of Markov processes on Riesz spaces.     

On the impact of conditional expectation estimators in portfolio theory

In this paper, we investigate the implications for portfolio theory of using conditional expectation estimators. First, we focus on the approximation of the conditional expectation within large-scale portfolio selection problems. In this context, we propose a new consistent multivariate kernel estimator to approximate the conditional expectation and it optimizes the bandwidth selection of kernel-type estimators. Second, we deal with the portfolio selection problem from the point of view of different non-satiable investors, namely risk-averse and risk-seeker investors. In particular, using a well-known ordering classification, we first identify different definitions of returns based on the investors preferences. Finally, for each problem, we examine several admissible portfolio optimization problems applied to the US stock market. The proposed empirical analysis allows us to evaluate the impact of the conditional expectation estimators in portfolio theory.     

Compact convergence of σ-fields and relaxed conditional expectation

The collection of sub-σ-fields of a Borel measure space when endowed with the topology of strong convergence is in general not a compact space. The paper offers a completion of this space which makes it compact. The elements which are added to the space are called relaxed σ-fields. A notion of relaxed conditional expectation with respect to a relaxed σ-field is identified. The relaxed conditional expectation is a probability measure-valued map. It is shown that the conditional expectation operator is continuous on the completion of the space. Other properties of conditional expectation are lifted to and interpreted in the relaxed framework. Received: 22 February 1999 / Revised version: 23 October 2000 / Published online: 8 May 2001     

条件期望作为初等算子在冯-代数上的描述

定义并研究了冯-代数.条件期望基于冯-代数的描述,即作为初等算子的良好性质,会较之一般代数简洁许多.这是因为冯-代数包含一些特殊的子代数.给出了此类代数上置信的初等条件期望的描述及其最小存在的充要条件.并且定义了指标冯-有限条件期望.作为以上结果的推论,得出了条件期望指标有限的充分必要条件和一个重要不等式.     

关于CIR模型中即期利率的条件密度及贴现债券定价(英文)

本文对CIR模型运用Kolgomorov向后方程给出即期利率的条件密度所满足的偏微分方程 ,并用谱方法将该密度表达成一个Laguerre型的正交级数之和 ,借助一个经验级数和公式 ,我们得出了该和式的第一类修正贝塞尔函数表达式 .同时 ,我们猜测贴现债券价格关于即期利率的特殊表达式 ,并通过求解两个一阶常微分方程验证了我们的猜测 .在文章的结尾 ,我们给出了贴现债券价格的条件期望和方差以反映必要的矩信息 .     

Computing conditional expectations of multidimensional diffusion processes

We study multidimensional diffusion processes and give an explicit representation for their conditional expectation. Starting from the solution formula for one dimensional stochastic differential equations found in Lanconelli and Proske [8], we compute the conditional expectation of a certain class of multidimensional diffusions without resorting to the Markov property of the process and therefore without requiring an explicit expression for the semi group associated to it.     

一个条件数学期望公式在期权定价中的应用

首先证明一个条件数学期望公式,然后建立股票价格的跳过程为Poisson过程,跳跃高度为常数时股票价格过程的随机微分方程,在风险中性的假设下,找等价鞅测度.利用鞅方法和已证明的条件数学期望公式,用较简单的数学推导得到了股票价格股从跳—扩散过程的欧式期权以及复合期权的定价公式.     

计算数学期望和概率的条件化方法

借助于条件数学期望和随机事件A的示性函数IA,通过对随机变量的适当"条件化"处理,应用全期望公式和推广的全概率公式,讨论了计算数学期望和概率的条件化方法.     

Nonparametric regression with interval-censored data

In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given.     

Bivariate Discrete Measures via a Power Series Conditional Distribution and a Regression

Problems of specifying bivariate discrete distributions by a conditional distribution and a regression function are investigated. A review of the known results, together with new characterizations involving conditional power series laws, is given. Also some remarks on a method making use of marginal and a conditional expectation are enclosed.     

Conditional expectations on Riesz spaces

Conditional expectations operators acting on Riesz spaces are shown to commute with a class of principal band projections. Using the above commutation property, conditional expectation operators on Riesz spaces are shown to be averaging operators. Here the theory of f-algebras is used when defining multiplication on the Riesz spaces. This leads to the extension of these conditional expectation operators to their so-called natural domains, i.e., maximal domains for which the operators are both averaging operators and conditional expectations. The natural domain is in many aspects analogous to L¹.     

On the Non-parametric Prediction of Conditionally Stationary Sequences

We prove the strong consistency of estimators of the conditional distribution function and conditional expectation of a future observation of a discrete time stochastic process given a fixed number of past observations. The results apply to conditionally stationary processes (a class of processes including Markov and stationary processes) satisfying a strong mixing condition, and they extend and bring together the work of several authors in the area of non-parametric estimation. One of our goals is to provide further justification for the growing practical application of non-parametric estimators in non-stationary time series and in other `non-i.i.d.' settings. Some arguments as to why such estimators should work very generally in practice, often in a nearly `optimal' way, are given. Two numerical illustrations are included, one with simulated data and the other with oceanographic data. An erratum to this article is available at .     

On Conditional Expectation Operators on L_p(\mu,X)(1\leq p \leq +\infinity,p\neq 2)

Some characterizations of the conditional expectation operators on Lebesgue-Bochner spaces L_p(\mu,X) are given, where $1\leq p<\infinity,p\neq 2$. Also an example is given to show that the characterizations of the conditional expectation operators on L_p(\mu, X) are different from that on L_p(\mu).Finally, a representation of the constant-preserving contractive projection on spaces L_p(\mu, X) is got when 0相似文献