Interpolating between random walk and rotor walk

We introduce a family of stochastic processes on the integers, depending on a parameter and interpolating between the deterministic rotor walk () and the simple random walk (). This p‐rotor walk is not a Markov chain but it has a local Markov property: for each the sequence of successive exits from is a Markov chain. The main result of this paper identifies the scaling limit of the p‐rotor walk with two‐sided i.i.d. initial rotors. The limiting process takes the form , where is a doubly perturbed Brownian motion, that is, it satisfies the implicit equation (1) for all . Here is a standard Brownian motion and are constants depending on the marginals of the initial rotors on and respectively. Chaumont and Doney have shown that Equation 1 has a pathwise unique solution , and that the solution is almost surely continuous and adapted to the natural filtration of the Brownian motion. Moreover, and . This last result, together with the main result of this paper, implies that the p‐rotor walk is recurrent for any two‐sided i.i.d. initial rotors and any .     

利用矩阵对角化求实递推式的通项

通过利用矩阵对角化理论探讨了一类实递推式的通项公式的求法.     

包含奇-偶下标第一类Chebyshev多项式的恒等式

主要研究了第一类Chebyshev多项式，给出了一类包含奇一偶下标第一类Chebyshev多项式求和的递推公式及恒等式．     

Fibonacci矩阵的探讨与应用

将Fibonacci数列推广到Fibonacci矩阵,利用Fibonacci矩阵的特殊性和矩阵的性质证明Fibonacci数列的性质。     

Invariant Measures for Set-Valued Dynamical Systems

A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set-valued map, there are several concepts which extend this idea of invariance for a measure. We prove that four such are equivalent. In particular, such relation invariant measures arise as projections from shift invariant measures on the space of sample paths. There is a similarly close relationship between the ideas of chain recurrence for the set-valued system and for the shift on the sample path space.

     

多维门限自回归序列的混合性

对多维门限自回归模型在给定阶数，门限及延迟参数的假定下，研究了模型所构成的Ｍａｒｋｏｖ链的常返性、遍历性及混合性。     

基于递归量化分析的表面肌电特征提取和分类

利用展拳、握拳和腕屈、腕伸时从前臂分别检测的两路表面肌电（surface electromyography,SEMG）信号,对四种动作进行了分类研究.先采用移动平均法（moving average,MA）和一阶差分法确定SEMG信号中对应的每个动作波形的起止点,再利用递归量化分析（recurrence quantification analysis,RQA）方法提取各种动作波形的非线性特征参量（确定率、递归率等）,由两路SEMG信号的这些特征参量构成特征矢量,输入BP（back propagation）神经网络,完成对不同动作的分类.研究结果表明,将利用递归量化分析得到SEMG信号的几种非线性参量作为特征值,对不同动作进行分类能够获得较高的分类准确率.     

On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results

A result by Elton⁽⁶⁾ states that an iterated function system

关于二次线性迭代序列的一些恒等式（Ⅱ）

利用形式幂级数的变换技巧，得到了涉及乘法数论函数及广义Ｆｉｂｏｎａｃｃｉ数、广义Ｌｕｃａｓ数的倒数和的若干恒等式，所给出的恒等式均具有显式形式；当退化到特殊情形时，可分别得到一类有意义的无穷和式。     

用神经网络构造鲁棒HMM＇s

对窗口神经网络（ＢＷＮＮ）与鲁棒ＨＭＭ’ｓ之间的关系作了新的探讨，指出了鲁棒ＨＭＭ’ｓ是循环的ＢＷＮＮ（ＲＢＷＮＮ）的特殊情况。讨论了由ＲＢＷＮＮ构造用于噪音环境下语音识别的组合ＨＭＭ’ｓ和二阶ＨＭＭ’ｓ的算法，给出了它们相应的网络结构。