随机康箍集的分形性质及分形渗流过程

本文综合介绍了两种随机康托集的分形性质和与之相关的随机过程的一些研究成果。     

一般从属过程占时测度的乘积测度的重分形结构

本文主要研究了两个相互独立的从零点出发的一般从属过程的轨道性质及它们的占时测度乘积的重分形谱．     

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...     

THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT （I）： MODEL,MARKOV PROPERTY,MOMENTS

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.     

随机康托集的概率性质

本文讨论了两类随机康托集。关于一类随机康托集，证明它们相交等价于稳定从属过程；关于另一类随机康托集，该文证明了由它们产生的随机过程的密度函数与稳定从属过程的密度函数有很大的相似性。     

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING （F） OR （B）

This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.     

定向集上B值Mil的收敛性及Riesz分解

本文主要研究定向集上B值mil的收敛性和Riesz分解。在[2]中M.Talagrand证明了:一个L~1有界的B值mil(X_n)_(n∈N)有唯一分解X_n=Y_n+Z_n,其中(Y_n)_(n∈N)为L~1有界鞅,(Z_n)_(n∈N)为mil且‖Z_n‖→0。本文将这一结果推广到定向集上,我们证明了:若(X_t,(?)_t,t∈J)为取值于可分Banach空间的mil,(_t)_(t∈J)满足Vitali条件V~1,则X_t有唯一分解X_t=Y_t+Z_t,其中(Y_t)_(t∈J)为L~1有界鞅,(Z_t)_(t∈J)为mil且。     

随机分形的测度性质

本文主要介绍随机过程样本轨道、Ｈａｗｋｅｓ模型、统计自相似集、统计自仿射集的测度性质，同时也将介绍一些离散分形的结果．文中还列出一些尚未解决的问题．     

Cantor集随机重排的Hausdorff测度

获得了Cantor集随机重排后所得的随机集的Hausdorff测度。