Some Notes on Large Deviations of Markov Processes

In this paper we shall characterize the large deviation principles (abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for the τ-topology, by means of a hyper-exponential recurrence property. A Lyapunov criterion for this type of recurrence property is presented. These results are applied to countable Markov chains, unidimensional diffusions, elliptic or hypoelliptic diffusions on Rienmannian manifolds. Several counter-examples are equally presented. Received July 20, 1998, Accepted March 25, 1999     

四类递推数列通项公式的推导及应用

介绍四类递推数列（列阶线性、二阶线性、一阶分式、二元一阶线性）通项公式的一般求法。     

某类K个参数指数族分布原点矩的递推公式

本给出某类K个参数指数族分布原点矩递推公式的方法，并举例进行说明。     

太阳高纬和低纬活动现象的混沌与分形特征

为了研究太阳高纬度和低纬度活动现象在南北半球的混沌与分形特征, 结合递归分析方法与Grassberger-Procaccia算法两种技术对1952年2月至1998年6月的极区光斑和黑子数目两种太阳磁活动指标进行了详细分析和比较. 主要结论如下: 1)由于太阳活动现象与磁场的时空演化密切相关, 导致太阳活动在南半球和北半球的混沌与分形特征具有不对称性, 太阳高纬度和低纬度活动现象的混沌与分形特征具有差异性; 2)太阳高纬度活动现象比低纬度活动现象具有更强的混沌程度和更复杂的分形结构, 其中太阳高纬度活动现象在北半球具有最强的混沌程度和最复杂的分形结构.     

关于不定方程3x(x+1)(x+2)(x+3)=7y(y+1)(y+2)(y+3)

运用递归序列和平方剩余的方法,证明了不定方程3x(x+1)(x+2)(x+3)=7y(y+1)(y+2)(y+3)仅有正整数解(x,y)=(4,3).     

Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces

We use a new multipoint iteration of at least R-order three to solve a nonlinear operator equation in a Banach space. Under standard Newton-Kantorovich assumptions, we establish two Kantorovich convergence theorems using a new system of recurrence relations. We also give some explicit error bounds for this iteration.     

半直线上随机环境中的可逗留随机游动的常返性

研究了在随机变量独立情形下,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,推广了Solomon的研究框架.     

一类随机环境中非紧邻的随机游动的常返性

本文对一类随机环境中非紧邻的随机游动(包括紧邻情况)进行了讨论,得到了一个便于计算的常返性准则,并通过举例说明用随机环境来代替其平均,其随机游动的性质可能完全相反。     

A recurrence formula with respect to the Cameron–Storvick type theorem of the 𝒯-transform

ABSTRACT

In this paper, we define a transform which has the kernel in its definition and a concept of derivative for functionals on Wiener space. We then establish some results and formulas for the transforms of functionals on Wiener space. We also establish the Cameron–Storvick type theorem for the transform. Finally, we obtain the recurrence formula for the transforms to evaluate formulas involving the multi-dimensional derivative.