优秀研究生学位论文题录展示

一维对称扩散过程的Dirichlet子空间

专 业: 概率论和数理统计  英文
关键词: 概率论 Dirichlet子空间 一维对称扩散
分类号: O21
形 态: 共 59 页 约 38,645 个字 约 1.849 M内容
阅 读: 全文阅读说明

内容摘要


This thesis mainly discusses Dirichlet spaces of one-dimensional diffusions and their regular subspaces.We show that the ε1-closure of an algebra of bounded functions in a Dirichlet space has Markovian property.This result gives a simple way to verify Markovian property.We also characterize all regular Dirichlet subspaces of Dirichlet space associated with a linear Brownian motion.The main results of this thesis include Theorem 1.1.1,Theorem 2.2.1,Theorem 2.3.1,Theorem 3.2.3 and Theorem 3.3.2.With the assumption that each point is regular,we characterize the local regular Dirichlet space of a symmetric diffusion on linear connected set I as foHows:

F={u∈L2I,m+k:

u is absolutely continuous with respect to s

and du/ds∈L3I,ds} εu,v=C∫I du/ds dv/ds ds+∫Iuxvxkdx,for u,v∈Fwhere m is the reference measure,k is the killing measure,s is the scale function,C is a positive constant number.We construct the associated symmetric diffnsion from a one dimensionalreflected or killed at the boundaries if finiteBrownian motion by a time change and a transform of state space if the killing measure k is zero.At the last,we give the sufficient and necessary conditions for a local regular Dirichlet form on L2I,mto be recurrent,transient and conservative……

全文目录


英文文摘
Acknowledgements
Chapter 0 Introduction and Preliminaries
Chapter 1 Algebraic structure on Dirichlet spaces
Chapter 2 On regular Dirichlet spaces of H1I and associated diffusions
Chapter 3 One dimensional local regular Dirichlet spaces and their regular subspaces
Bibliography

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