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1.
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. 相似文献
2.
The conditional supremum of a random variable X on a probability space given a sub--algebra is defined and proved to exist as an application of the Radon–Nikodym theorem in L
\infty. After developing some of its properties we use it to prove a new ergodic theorem showing that a time maximum is a space maximum. The concept of a maxingale is introduced and used to develop the new theory of optimal stopping in L
\infty and the concept of an absolutely optimal stopping time. Finally, the conditional max is used to reformulate the optimal control of the worst-case value function. 相似文献
3.
讨论半群上条件正定函数的扩张问题.得到一个扩张定理.作为应用,得到有界扩张定理和Pontryagin空间上量子力学的一个基本定理. 相似文献
4.
We show that the conditional central limit theorem can take place for a stationary process defined on a nonergodic dynamical
system while this last does not satisfy the central limit theorem for any ergodic component. There exists an ergodic Markov
chain such that the conditional central limit theorem is satisfied for an invariant measure but fails to hold for almost all
starting points.
相似文献
5.
条件扩散过程的生命时与条件Gauge 总被引:2,自引:0,他引:2
本文给出了有界的Lipschitz区域D内的条件扩散过程的生命时T_D的一个渐近估计,由此给出了Gauge与条件Gauge为有穷或无穷的谱条件,并得出了Gauge定理与条件Gauge定理。 相似文献
6.
B. L. S. Prakasa Rao 《Annals of the Institute of Statistical Mathematics》2009,61(2):441-460
Some properties of conditionally independent random variables are studied. Conditional versions of generalized Borel-Cantelli
lemma, generalized Kolmogorov’s inequality and generalized Hájek-Rényi inequality are proved. As applications, a conditional
version of the strong law of large numbers for conditionally independent random variables and a conditional version of the
Kolmogorov’s strong law of large numbers for conditionally independent random variables with identical conditional distributions
are obtained. The notions of conditional strong mixing and conditional association for a sequence of random variables are
introduced. Some covariance inequalities and a central limit theorem for such sequences are mentioned. 相似文献
7.
W. van Zuijlen 《Journal of Theoretical Probability》2018,31(2):1058-1096
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of probability measures on the product space that satisfies a large deviation principle, we present necessary and sufficient conditions for the conditional probabilities under these measures to satisfy a large deviation principle. The arguments of these conditional probabilities are assumed to converge. A way to view regular conditional probabilities as a special case of product regular conditional probabilities is presented. This is used to derive conditions for large deviations of regular conditional probabilities. In addition, we derive a Sanov-type theorem for large deviations of the empirical distribution of the first coordinate conditioned on fixing the empirical distribution of the second coordinate. 相似文献
8.
Relation between association and conditional association is answered, several examples show that the association of random variables does not imply the conditional association, and vice versa. Several fundamental properties of conditional associated random variables are developed, which extend the corresponding ones under the non-conditioning setup. By means of these properties, some conditional Hájek-Rényi type inequalities, a conditional strong law of large numbers and a conditional central limit theorem stated in terms of conditional characteristic functions are established, which are conditional versions of the earlier results for associated random variables, respectively. In addition, some lemmas in the context are of independent interest. 相似文献
9.
10.
From the ordinary notion of negative association for a sequence of random variables, a new concept called conditional negative
association is introduced. The relation between negative association and conditional negative association is answered, that
is, the negative association does not imply the conditional negative association, and vice versa. The basic properties of
conditional negative association are developed, which extend the corresponding ones under the non-conditioning setup. By means
of these properties, some Rosenthal type inequalities for maximum partial sums of such sequences of random variables are derived,
which extend the corresponding results for negatively associated random variables. As applications of these inequalities,
some conditional mean convergence theorems, conditionally complete convergence results and a conditional central limit theorem
stated in terms of conditional characteristic functions are established. In addition, some lemmas in the context are of independent
interest. 相似文献
11.
G.Y.H Chi 《Journal of multivariate analysis》1973,3(1):71-92
Let (Ω, Σ, P) be a fixed complete probability space, the real Schwartz space, and its strong dual. and are partially ordered by and respectively, where is the positive cone of nonnegative functions in and its dual in . is a strict -cone and is normal, where is the family of all bounded subsets of . If X, Y are two random Schwartz distributions, then X ≤ Y if and only if Y(ω) ? X(ω) ∈ for almost all . Integrability of random Schwartz distributions and properties of such integrals are discussed. The monotone convergence theorem, the dominated convergence theorem, and Fatou's lemma are proved. The existence of conditional expectations of integrable random Schwartz distributions relative to a given sub σ-field of Σ is shown. Properties of conditional expectations are discussed and the conditional form of the monotone convergence theorem is proved. Sub(super)-martingale sequences are defined via the partial order relations introduced above, and a convergence theorem is given. The notion of a potential is introduced and the Riesz decomposition theorem is proved. 相似文献
12.
13.
Asgar Jamneshan Michael Kupper Martin Streckfuß 《Set-Valued and Variational Analysis》2018,26(4):947-973
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In particular, this extends the usual representation results for separable spaces. 相似文献
14.
Ellen Hisdal 《Fuzzy Sets and Systems》1978,1(4):283-297
Relations from the theory of probability are compared with corresponding relations in the theory of possibility. Because of the special properties of the min operator, the values of the conditional possibilities are much more similar to those of the joint possibilities than is the case in connection with probabilities. When the joint possibilities are given, the solution for the conditional possibilities is not always unique. It is shown that we must distinguish between noninteraction and independence of fuzzy or possibilistic variables. For purposes of inference, relations representing conditional possibility distributions should be used. 相似文献
15.
M. F. Sukhinin 《Mathematical Notes》1973,14(3):775-779
A theorem of Lyusternik on conditional extrema of a differentiable functional defined on a Banach space is generalized to the case of a topological linear space.Translated from Matematicheskie Zametki, Vol. 14, No. 3, pp. 375–382, Septembers 1973. 相似文献
16.
Selim Tuncel 《Israel Journal of Mathematics》1981,39(1-2):101-112
We use pressure to obtain invariants for bounded-to-one block homomorphisms between Markov shifts. These invariants enable
us to show that if there is a bounded-to-one block homomorphism between Bernoulli shifts given by probability vectorsp andq thenq may be obtained fromp by a permutation. The invariants may be viewed as conditional pressures; a convergence theorem for eigenmeasures of Ruelle
operators motivates the definition of conditional pressure and helps establish our invariants for regular isomorphism of Markov
shifts. It follows that Bernoulli shifts given by probability vectorsp andq are regularly isomorphic iffq is a permutation ofp. We employ our invariants also in the context of a finite equivalence. Finally we indicate that ratio variational principles
yield further invariants. 相似文献
17.
From the ordinary notion of linearly negative quadrant dependence for a sequence of random variables, a new concept called conditionally linearly negative quadrant dependence is introduced. The relation between the two kinds of dependence is answered by examples, that is, the linearly negative quadrant dependence does not imply the conditionally linearly negative quadrant dependence, and vice versa. The fundamental properties of conditionally linearly negative quadrant dependence are developed, which extend the corresponding ones under the non-conditioning setup. By means of these properties, some conditional exponential inequalities, conditionally complete convergence results and a conditional central limit theorem stated in terms of conditional characteristic functions are established. 相似文献
18.
Mitri Kitti 《Mathematical Methods of Operations Research》2013,78(1):77-100
This paper introduces conditional Markov strategies in discrete-time discounted dynamic games with perfect monitoring. These are strategies in which players follow Markov policies after all histories. Policies induced by conditional Markov equilibria can be supported with the threat of reverting to the policy that yields the smallest expected equilibrium payoff for the deviator. This leads to a set-valued fixed-point characterization of equilibrium payoff functions. The result can be used for the computation of equilibria and for showing the existence in behavior strategies. 相似文献
19.
Wen-Chi Kuo 《Journal of Mathematical Analysis and Applications》2005,303(2):509-521
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. 相似文献
20.