Mathematical Sciences: Stochastic Processes

数学科学：随机过程

• 批准号: 9207276
• 负责人: Michael Marcus
• 金额: $ 25.38万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207276&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stochastic; Processes

Professors Marcus and Rosen will continue their investigations of the relationship between Gaussian processes and the local times of symmetric Markov processes put into evidence by the Dynkin Isomorphism Theorem. A compact form of this Theorem will be used in an attempt to obtain Borell type inequalities for local times. Analogous to their recent work which shows the equivalence of sample path properties of the local times of a symmetric Markov process and an associated Gaussian process they will study the relationship between continuous additive functionals of a symmetric Markov process indexed by measures and an associated class of Gaussian chaoses indexed by measures. This will require an investigation into measure indexed Gaussian processes and chaoses in general. They will also try to extend their recent work on the law of the iterated logarithm for the local times of symmetric Levy processes and random walks to cover the interesting case of recurrent random walks on a two dimensional integer lattice. Professor Marcus and Rosen will continue their investigations of the relationship between Gaussian Processes and the local times of symmetric Markov processes. Until recently these stochastic processes were not considered to be related at all, except in the case of Brownian motion, a relationship was implied by a recent isomorphism theorem of Dynkin. This isomorphism has been exploited by Professors Marcus and Rosen to show that there are deep connections between these two fundamental classes of stochastic processes, both of which serve as models in countless applications to continuous time random phenomena. This research could lead to significant new knowledge about our random environment.

马库斯教授和罗森教授将继续他们的 研究高斯过程与 对称马氏过程的局部时 Dynkin同构定理这个定理的一个紧凑形式 将被用来试图获得Borell型不等式， 当地时间。 类似于他们最近的工作， 局部时样本路径性质的等价性 对称马尔可夫过程和相关高斯过程， 将研究连续可加性 一个对称马尔可夫过程的泛函指标的措施和 一个关联类的高斯混沌指标的措施。这 将需要对测量指数高斯的调查 过程和混沌。他们还将努力扩大 他们最近的工作对法律的重对数为 对称Levy过程和覆盖随机游动的局部时 一个有趣的例子， 维整数格 马库斯教授和罗森将继续 研究高斯过程与 对称马尔可夫过程的局部时 直到最近 这些随机过程被认为是不相关的， 所有的，除了布朗运动的情况下，一个关系是 由Dynkin最近的同构定理所暗示。 这 Marcus和罗森教授利用同构性， 表明这两者之间有着很深的联系 基本类的随机过程，这两个服务 作为模型在无数的应用中， 现象。 这项研究可能会带来重要的新知识 我们的随机环境。