H值多参数扩散过程的大偏差与泛函重对数律

本文得到Ｈ值多参数扩散过程的Ｗｅｎｔｚｅｌｌ－Ｆｒｅｉｄｌｉｎ估计，并且利用大偏差估计讨论扩散过程的泛函重对数律．     

关于可逆反应-扩散过程大偏差的一个注记

本文考虑一类可逆反应－扩散过程，并证明了有限位置集上时刻t前的平均粒子数的大偏差原理．这一结果不能由已证明了的经验分布的大偏差原理通过压缩原理得到．     

扩散过程在Hlder范数下的局部Strassen重对数律

在该文中,作者应用扩散过程在Holder范数下的大偏差得到了扩散过程在Holder范数下的局部Strassen重对数律．并且还得到了重It■积分的泛函重对数律．     

扩散过程关于（r，p）－容度的大偏差

本文证明扩散过程关于（ｒ，ｐ）－容度服从大偏差原理，作为此结果的一个应用，我们证明扩散过程的拟泛函重对数律成立．     

退火过程的轨道性质

本文中我们建立了一些非时齐过程的大偏差性质．利用大偏差技术，我们找到了退火过程的ω－极限集．     

一类Levy过程和自相似Markov过程的Packing维数结果

本文得到了一般Levy过程X（t）的象集X（E）的packing维数的一致上界当X（t）是暂留对称的或X（t）是subordinator时，可得到DimX（E）的一致下界．并用这些结果得到了一类自相似马氏过程象集的packing维敏．     

关于一维随机环境中非最近邻居的随机游动的尾估计

本文研究了一类一维随机环境中非最近邻居的随机游动,在暂留的情况下,给出了它的速度,并进一步研究了其偏离速度的尾概率的估计,证明了这个尾概率是以多项式的速率衰减,给出了这个指数．我们的结果是Zeitouni及其合作者在1996年的文章中结果的推广．在证明中我们用到了随机矩阵乘积的大偏差估计及随机环境中多型分支过程的总人口数的尾概率估计和矩量估计．     

高维扩散过程扩散系数估计的中偏差

本文考虑高维扩散过程的大偏差.对于高维扩散过程dX(t)=σ(t)dB(t),(其中σ(t)未知),我们讨论其平方变差过程[X]t=∫0t(σσ*)(s)ds的估计的大偏差及中偏差.通过利用Gartner-Ellis定理,得到了上述估计在固定时刻t=1时的中偏差;同时通过计算其对数矩生成函数的Fenchel-Legendre变换,得到其速率函数的显式表达.     

扩散过程在Hlder范数下的大偏差(英文)

本文利用一种推广的收缩原理，证明扩散过程在Ｈｌｄｅｒ范数下大偏差原理仍成立     

扩散过程的拟必然局部Strassen重对数律

应用大偏差,得到了扩散过程和重随机积分的拟必然局部Strassen重对数律.     

Some variational formulas on additive functionals of symmetric Markov chains

For symmetric continuous time Markov chains, we obtain some formulas on total occupation times and limit theorems of additive functionals by using large deviation theory.

     

On the Local Times of Transient Random Walks

We study the properties of the local and occupation times of certain transient random walks. First, our recent results concerning simple symmetric random walk in higher dimension are surveyed, then we start to establish similar results for simple asymmetric random walk on the line.     

Large deviations in total variation of occupation measures of one-dimensional diffusions

For one-dimensional diffusion processes, we find an explicit necessary and sufficient condition for the large deviation principle of the occupation measures in the total variation and of local times in L¹$L^1$.     

Occupation time theorems for a class of one-dimensional diffusion processes

Summary The long time asymptotic behavior of the occupation times on a half line is studied for a class of one-dimensional diffusion processes whose excursion intervals have very heavy tail probability     

Continuity of Harmonic Functions for Non-local Markov Generators

We consider a class of pure jump Markov processes in ${\mathbb R}^d$ whose jump kernels are comparable to those of symmetric stable processes. We prove a support theorem, a lower bound on the occupation times of sets, and show that we can approximate resolvents using smooth functions.     

The problem of the most visited site in random environment

We prove that the process of the most visited site of Sinai's simple random walk in random environment is transient. The rate of escape is characterized via an integral criterion. Our method also applies to a class of recurrent diffusion processes with random potentials. It is interesting to note that the corresponding problem for the usual symmetric Bernoulli walk or for Brownian motion remains open. Received: 17 April 1998     

On the Joint Law of the Occupation Times for a Diffusion Process on Multiray

For a diffusion process on multiray, the joint law of the occupation times on rays is studied. Two important formulae, the generalized Williams formula and the double Laplace transform formula, are proved. A limit theorem for the joint law and a representation of the density function are also discussed. The proofs are based on Itô’s excursion theory for Markov processes.     

Boundary trace of reflecting Brownian motions

We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.Mathematics Subject Classification (2000):Primary 60G17, 60J60, Secondary 28A80, 30C35, 60G52, 60J50     

A Large Deviation Principle for Symmetric Markov Processes with Feynman–Kac Functional

We establish a large deviation principle for the occupation distribution of a symmetric Markov process with Feynman–Kac functional. As an application, we show the L ^p -independence of the spectral bounds of a Feynman–Kac semigroup. In particular, we consider one-dimensional diffusion processes and show that if no boundaries are natural in Feller’s boundary classification, the L ^p -independence holds, and if one of the boundaries is natural, the L ^p -independence holds if and only if the L ²-spectral bound is non-positive.     

Convergence rates for rank-based models with applications to portfolio theory

We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are obtained using Transportation Cost-Information inequalities for Markov processes. We work out various applications to the rank-based abstract equity markets used in Stochastic Portfolio Theory. For example, we produce quantitative bounds, including constants, for fluctuations of market weights and occupation times of various ranks for individual coordinates. Another important application is the comparison of performance between symmetric functionally generated portfolios and the market portfolio. This produces estimates of probabilities of “beating the market”.