马氏环境中马氏链的一个概率不等式及其应用

本文研究了马氏环境中马氏链构成的随机变量之和的概率不等式问题.利用了结尾的方法,获得了马氏环境中马氏链构成的随机变量之和的尾部概率不等式,作为结果的应用,给出了将过程限制在(S,S∩F,PS)上的强大数定律.文中提出的方法和结果对研究独立的随机变量之和的大样本性质是十分有用的.     

马氏决策过程平均准则最优不等式综述

对平均准则的讨论一直是马氏决策过程研究的热点之一，近几年已从最优方程推广到最优不等式。本文系统地了介绍最优不等式的提出及其发展思路，目前已取得的成果等，同时也指出了有待于进一步研究的问题。     

非时齐马氏过程的Liggett-Stroock不等式

本文将时齐马氏过程中重要的代数不等式Liggett-Stroock不等式推广到非时齐马氏过程中,建立了非时齐马氏过程的转移半群与Liggett-Stroock不等式之间的关系.     

基于谱隙的依全变差指数式收敛速度估计

利用与谱隙作比较的手法，本文研究可逆马氏过程依全变差的指数式收敛速度．我们证明在相当一般的情况下，只要对初分布略加限制，则此速度以谱隙为下界．进而，对于紧空间情形或生灭过程或半直线上的扩散，我们证得此速度等于谱隙．     

随机利率下马氏调控Pascal模型破产概率的估计

本文研究随机环境下带随机利率的复合Pascal风险模型破产概率上界估计,对利率和费率分别按两个马氏环境变化的Pascal风险模型,给出破产概率满足的不等式.     

报酬无界的平均准则马氏决策过程

本文对可数状态集、非空决策集、报酬无界的平均准则马氏决策过程，提出了一组新的条件，在此条件下存在（ε）最优平稳策略，且当最优不等式中的和有定义时最优不等式也成立。     

对连续状态马氏链Dobrushin不等式的一个证明

本文先利用Dobrushin系数的定义和Fubini定理证明一个不等式,相应地给出连续状态马氏链Dobrushin不等式的一个证明.     

状态可数的马氏环境中马氏链函数的强大数定律

讨论了马氏双链与随机环境中马氏链的关系．在此基础上，研究了具有离散参量的马氏环境中马氏链函数的强大数定律，并且给出了直接加于链和过程样本函数上的充分条件．     

非时齐马氏过程的对数Sobolev不等式

本文将时齐马氏过程的经典对数Sobolev不等式推广到非时齐马氏过程,建立了非时齐马氏过程的转移半群与对数Sobolev不等式之间的关系.     

马氏环境中的马氏链与马氏双链

本文研究了马氏环境中的马氏链,利用马氏双链的性质,得到了马氏环境中的马氏链回返于小柱集上的概率的若干估计式.     

Logarithmic Sobolev,isoperimetry and transport inequalities on graphs

In this paper,we study some functional inequalities(such as Poincaré inequality,logarithmic Sobolev inequality,generalized Cheeger isoperimetric inequality,transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of(random) path method.We provide estimates of the involved constants.     

Hoeffding's inequality for Markov processes via solution of Poisson's equation

We investigate Hoeffding's inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the inequalities are obtained via the solution of Poisson's equation. The results are further illustrated with applications to queueing theory and reective diffusion processes.     

无界拉普拉斯算子下图上的泛函不等式

本文探讨图上的泛函不等式,并且在无界拉普拉斯算子的意义下,利用图的完备性和图上超压缩性的性质,证明了图上对数Sobolev不等式的成立,以及超压缩性与图上Nash不等式的等价关系.     

Wang's Harnack inequalities for space–time white noises driven SPDEs with two reflecting walls and their applications

In this paper, we establish Wang's Harnack inequalities for Gaussian space–time white noises driven the stochastic partial differential equation with double reflecting walls, which is of the infinite dimensional Skorokhod equation. We first establish both the Harnack inequality with power and the log-Harnack inequality for the special case of additive noises by the coupling approach. Then we investigate the log-Harnack inequality for the Markov semigroup associated with the reflected SPDE driven by multiplicative noises using the penalization method and the comparison principle for SPDEs. As their applications, we study the strong Feller property, uniqueness of invariant measures, the entropy-cost inequality, and some other important properties of the transition density.     

Functional inequalities in non-Archimedean normed spaces

In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in non-Archimedean Banach spaces.     

A Generalization of Poincaré and Log-Sobolev Inequalities

A generalized Beckner-type inequality interpolating the Poincaré and the log-Sobolev inequalities is studied. This inequality possesses the additivity property and characterizes certain exponential convergence of the corresponding Markov semi-group. A correspondence between this inequality and the so-called F-Sobolev inequality is presented, with the known criteria of the latter applying also to the former. In particular, an important result of Lataa and Oleszkiewicz is generalized.     

Minimization principles for elliptic hemivariational inequalities

In this paper, we explore conditions under which certain elliptic hemivariational inequalities permit equivalent minimization principles. It is shown that for an elliptic variational–hemivariational inequality, under the usual assumptions that guarantee the solution existence and uniqueness, if an additional condition is satisfied, the solution of the variational–hemivariational inequality is also the minimizer of a corresponding energy functional. Then, two variants of the equivalence result are given, that are more convenient to use for applications in contact mechanics and in numerical analysis of the variational–hemivariational inequality. When the convex terms are dropped, the results on the elliptic variational–hemivariational inequalities are reduced to that on “pure” elliptic hemivariational inequalities. Finally, two representative examples from contact mechanics are discussed to illustrate application of the theoretical results.     

Inequalities and Convergence Concepts of Fuzzy and Rough Variables

It is well-known that Markov inequality, Chebyshev inequality, Hölder's inequality, and Minkowski inequality are important and useful results in probability theory. This paper presents the analogous inequalities in fuzzy set theory and rough set theory. In addition, sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper presents four types of convergence concept of fuzzy/rough sequence: convergence almost surely, convergence in credibility/trust, convergence in mean, and convergence in distribution. Some mathematical properties of those new convergence concepts are also given.     

半序线性空间上线性泛函的两个Gr\"{u}ss型不等式$^{}$

证明了半序线性空间上线性泛函的两个Gr\"{u}ss型不等式, 并由此给出了Karamata型积分不等式的一种推广形式, 得到了一个新的Gr\"{u}ss型积分不等式及关于傅立叶系数的两个不等式. 最后利用所得结论研究了关于矩阵及线性算子的一些Gr\"{u}ss型不等式.     

关于两个新型Hilbert不等式的推广

众所周知,Hilbert不等式是一个有重要应用的不等式,1998年,B．G．Pachpatte给出了类似Hilbert级数不等式的两个新不等式,本文的主要工作是推广了这两个新个新不等式。