关于滑动相对熵的若干极限性质

引入滑动似然比和滑动相对熵等概念,讨论了滑动相对熵的若干渐近性质.主要结果是,获得了随机变量任意状态的相对频率与滑动相对熵之间的关系,并且给出了滑动相对熵基于相对频率的上界的估计.作为推论,得到了随机序列滑动平均的强大数定理.     

伪轨跟踪与一致正熵

本文对于满足伪轨跟踪性质的紧致度量空间上的连续满射f，给出了f具有一致正熵的几个充要条件和一个必要条件．     

不变测度,比例极限和Martin边界

In this article the notion of quasi-symmetry is introduced. It is proved that the quasisymmetry is equivalent to the uniqueness of invariant measure of Levy processes in some senseMoreover,the relationship between ratio limits and invariant measures is studied.     

符号空间及逆极限空间上的正混沌

本文推广Ｌｉ－Ｙｏｒｋｅ混沌定义,给出正混沌的定义,得到一类描述正混沌的符号动力 系统．并证明紧致度量空间上的连续映射正混沌的充要条件是其逆极限空间上的移位映射是 正混沌的．     

相对熵密度与任意二进信源的若干极限性质

相对熵密度与任意二进信源的若干极限性质刘文（河北工学院基础部，天津３００１３０）杨卫国（河北煤炭建工学院基础部，邯郸０５６０３８）ＲＥＬＡＴＩＶＥＥＮＴＲＯＰＹＤＥＮＳＩＴＹＡＮＤＳＯＭＥＬＩＭＩＴＰＲＯＰＥＲＴＩＥＳＯＦＡＲＢＩＴＲＡＲＹＢＩＮＡＲ...     

关于有限马氏链相对熵密度和随机条件熵的一类极限定理

本文引进有限非齐次马链随机条件熵的概念，研究这个概念与相对熵密度的关系，并通过数列的绝对平均收敛的概念给出了有限非齐次马氏链的相对频率，相对熵密度和平均随机条件熵ａ．ｅ收敛于常数及有限非齐次马氏链熵率存在的条件。     

非线性抛物问题熵解的某些定性性质

本文研究了非线性抛物问题熵解的正性依赖于初始资料和方程右端项的正性以及熵解的稳定性依赖于方程右端项的弱L1摄动.     

非线性抛物问题熵解的某些定性性质

本文研究了非线性抛物问题熵解的正性依赖于初始资料和方程右端项的正性以及熵解的稳定性依赖于方程右端项的弱 Ｌ~１摄动．     

不变测度的Hausdorff维数和熵的关系

得到了紧致度量空间上可扩同胚的不变测度的Hausdorff维数和熵的几个关系式 ,并找到了熵为零的一个充要条件 .     

测度的上局部熵和集合的类Bowen熵

设f为度量空间(x,d)上的连续映射,该文主要讨论了x的任意子集关于f的类Bowen熵可以通过(x,d)上测度的上局部熵估计.     

加权复合算子的不变测度

本文研究复的可分 Hilbert L2 ( S,Σ,μ)加权复合算子 Tf(· ) =w(· ) f( h(· ) )存在平方可积的不变测度的条件 ,并且证明关于 T不变的平方可积的测度支集全体所张成的闭子空间等于 T的幺模特征向量全体所张成的闭子空间     

Fine-grained and coarse-grained entropy in problems of statistical mechanics

We consider dynamical systems with a phase space Γ that preserve a measure μ. A partition of Γ into parts of finite μ-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on Γ and generalizes the usual (ordinary or fine-grained) Gibbs entropy. We study the approximation properties of the coarse-grained entropy under refinement of the partition and also the properties of the coarse-grained entropy as a function of time. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 120–137, April, 2007.     

Invariant Measure and a Limit Theorem for Some Generalized Gauss Maps

Continued fractions w.r.t. a specified class of numbers is considered. The invariant measures of the corresponding transformations are identified connecting the continued fractions with geodesics on the upper half plane. A problem of convergence in distribution of sums of the coefficients of the continued fraction is also considered.     

逆极限空间上渐近伪轨跟踪性质

The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP.     

Invariant subspaces for positive operators on locally convex solid Riesz spaces

We prove that an x₀-quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of Abramovich, Aliprantis and Burkinshaw [J. Funct. Anal. 115 (1993) 418424] is also given.     

On shadowing property for inverse limit spaces

We study here the G-shadowing property of the shift map σ on the inverse limit space X _f, generated by an equivariant self-map f on a metric G-space X.      

Bounds for the uniform deviation of empirical measures

If X₁,…,X_n are independent identically distributed R^d-valued random vectors with probability measure μ and empirical probability measure μ_n, and if $\text{a}$ is a subset of the Borel sets on R^d, then we show that P{sup_{A∈$\text{a}$}|μ_n(A)?μ(A)|≥ε} ≤ cs($\text{a}$, n²)e^?2n∈2, where c is an explicitly given constant, and s($\text{a}$, n) is the maximum over all (x₁,…,x_n) ∈ R^dn of the number of different sets in {{x₁…,x_n}∩A|A ∈$\text{a}$}. The bound strengthens a result due to Vapnik and Chervonenkis.     

Absolutely continuous invariant measures for random maps with position dependent probabilities

A random map is discrete-time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process. Usually the map τ_k is chosen from a finite collection of maps with constant probability p_k. In this note we allow the p_k's to be functions of position. In this case, the random map cannot be considered to be a skew product. The main result provides a sufficient condition for the existence of an absolutely continuous invariant measure for position dependent random maps on [0,1]. Geometrical and topological properties of sets of absolutely continuous invariant measures, attainable by means of position dependent random maps, are studied theoretically and numerically.     

On generalized measures of entropy and dependence

Various authors have studied extensions of Shannon’s entropy but their inferential properties and applications in applied sciences have not invited proper attention from researchers. In the present paper we explore the motivation and implication of using various classes of the generalized entropies and conditional entropies. We evaluate β-class and (α, β)-class entropies for multivariate normal density function. We also obtain the measures of dependence in terms of the classes of generalized entropies.