延拓分支过程

本给出一类连续时间延拓分支过程Ｘ（ｔ）的大偏差原理成立的条件以及有关的一类上鞅。     

集值上鞅的轨道正则性

本文证明了在有限维Ｂａｎａｃｈ空间中，任一闭凸集值鞅（在ｋ－收敛意义下）存在右连左极修正．     

Li-Yorke混沌的充要条件

本文给出了Ｌｉ－Ｙｏｒｋｅ混沌的一个充要条件．     

ω-聚点及其一些好的性质

在LF拓扑空间中,引入ω-聚点的概念,这一概念克服了以往聚点的缺点,使得对任意的LF集A,B,A-=A∨Adω和(A∨B)dω=Adω∨Bdω同时成立。     

集值L^1—极限鞅的集值鞅逼近及其收敛性

本文证明了集值Ｌ~１－极限鞅的集值鞅逼近定理,并利用此结果以及集值鞅的收敛性结果讨论了集值Ｌ~１－极限鞅的收敛性．     

一类半鞅样本轨道的Fractal性质

本文用Ｈａｕｓｄｏｒｆｆ维数刻画了一类半这样本轨道的Ｆｒａｃｔａｌ性质，并由此研究了Ｂｒｏｗｎ运动与有界变差过程的碰撞问题．     

集值下(上)鞅的 Doob 分解

本文研究集值下(上)鞅的 Doob 分解.我们得到一些确保 Doob 分解存在的充要条件,并给出例子说明并非所有集值下(上)鞅都有 Doob 分解.     

集值L1极限鞅导出的集值测度

讨论集值L1极限鞅的一些性质,在此基础上,研究集值L1极限鞅导出的集值测度及其性质.     

动力系统方法应用到一类非线性椭圆方程的基态解

本文将动力系统理论的思想和方法应用到一类具有Sobolev次临界指数的非线性椭圆型方程,通过吸引子的存在性及其结构分析来研究稳态方程基态解的存在性及其渐近性态.这一方法的细致应用,不仅需要在理论和应用上创新,而且必将为相关领域的研究提供新的研究途径和思想方法,对非线性分析和无穷维动力系统的理论和应用发展产生积极的推动作...     

泊松点过程的若干大偏差估计

本文给出泊松点过程下列三种极限行为的大偏差估计：（１）高密度情形；（２）低密度情形和（３）标度变换下极限情形。     

Sample Path Properties of a Class of Operator Stable Processes

Abstract

Let X = {X(t), t ? ?₊} be an operator stable Lévy process on ? ^d with the exponent B, where B is a diagonal matrix. In the present paper, we consider the asymptotic behavior of the first passage time out of a sphere, and of the sojourn time in a sphere. We shall also determine the exact Hausdorff measure function for the range of X over unit time interval [0, 1].     

On Symmetric Stable-Like Processes: Some Path Properties and Generators

We derive some path properties of symmetric stable-like processes constructed via Dirichlet form theory and then sufficient conditions in order that the generators of the forms contain a nice functions space, are given.     

Path Properties of Dilatively Stable Processes and Singularity of Their Distributions

First, we present some results about the Hölder continuity of the sample paths of so-called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a corollary, we obtain that the most important (H, δ)-dilatively stable limit processes (e.g., the LISOU and the LISCBI processes, see [4 Iglói , E. 2008 . Dilative Stability, Ph.D. Thesis, University of Debrecen, Faculty of Informatics. http://www.inf.unideb.hu/valseg/dolgozok/igloi/dissertation.pdf  [Google Scholar]]) almost surely have a local Hölder exponent H. Next we prove that, under some slight regularity assumptions, any two dilatively stable processes with stationary increments are singular (in the sense that their distributions have disjoint supports) if their parameters H are different. We also study the more general case of not having stationary increments. Throughout the article, we specialize our results to some basic dilatively stable processes such as the above-mentioned limit processes and the fractional Lévy process.     

On Some Path Properties of Symmetric Stable-Like Processes for One Dimension

We show that a symmetric stable-type form becomes a Dirichlet form in the wide sense under a quite mild assumption and give a necessary and sufficiently condition that the domain contains the family of all uniformly Lipschitz continuous functions with compact support. Moreover we give some path properties of the corresponding Markov processes (we call the processes symmetric stable-like processes) in one dimension such as exceptionality of points and recurrence of the processes. We then note that the recurrence of the processes depend on the behavior of the index functions at the infinity.     

拟正则保正型过份函数的积分表示及h-结合过程的轨道性质

本文讨论拟正则保正型α-过份函数的积分表示,证明拟正则保正型（ε,D（ε））的任意α-过份函数u均可表示为εα（u,v）=∫vdμ,v∈D（ε）,μ是E上的σ有限测度。并证明（ε,D（ε））的h-结合过程是暂留的和非保守的。     

Function Spaces as Path Spaces of Feller Processes

Let {X_t}_{t ≥ 0} be a Feller process with infinitesimal generator (A, D(A)). If the test functions are contained in D(A), —A |C^∞_c (ℝⁿ) is a pseudo–differential operator p(x, D) withsymbol p(x, ξ). We investigate local and global regularity properties of the sample paths t ↦ X_t in terms of (weighted) Besov B^s_pq (ℝ, ρ) and Triebel–Lizorkin F^s_pq (ℝ, ρ) spaces. The parameters for these spaces are determined by certain indices that describe the asymptotic behaviour of the symbol p(x, ξ). Our results improve previous papers on Lévy [5, 9] and Feller processes [22].     

Some Properties of CIR Processes

Abstract

This article derives some properties of variants of squared Bessel processes known as CIR processes in the finance literature. We derive the transition probability density function of a square-root process and compute the resolvent density of CIR processes. As a consequence, we derive the density of CIR processes sampled at an independent exponential time. Moreover, we derive explicit expressions of the Laplace transforms (LTs) of first hitting times by martingale methods.     

约束最优路线问题的模拟退火解法

本以１９９８年全国大学生数模竞赛中的Ｂ题（即“灾情巡视路线”）为例,介绍一种最优路线问题的方法－－模拟退火法＾「１」。该法对旅行推销员、中国邮递员等问题,即使有约束条件,也能求得较好的近似解,具有适用范围广和可拓展的优点。     

Serial Dependence Properties of Linear Processes

The paper describes a class of models rather more general than the ARIMA processes of Box and Jenkins, and surveys recently achieved results for their serial dependence behaviour. These properties are obtained analytically, from simulation and by direct computation-either approximately or exactly. The paper concentrates on the expectations of serial covariances and the problem of distinguishing between nearly non-stationary models and homogeneous non-stationary approximations to them-in particular, for a specific pair of ARMA(1,1) and IMA(1,1) processes.     

拟单位根过程的渐近性质

West[4],Phillips[3]的关于AR（1）过程的一些有关渐近正态性的结果推广到了拟整过程，所得的结果更具一般性，从而可用来进行单位根据检验及协整检验的功效分析。