Asymptotic Analysis of Probability Laws and Path Behaviors for Markov Processes

马尔可夫过程的概率定律和路径行为的渐近分析

• 批准号: 09640293
• 负责人: SHIMURA Michio
• 金额: $ 1.6万
• 依托单位: Faculty of Science, Toho University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640293/
• 关键词: random walk; infinite particle system; stochastic numerical analysis; Laplacian on a graph; harmonic map; spectral structure; biharmonic operator; operator algebra; グラフの上のラプラシアン; 碓率数値解析; モンテカルロ解析; 無縁Brown粒子系; スペクトル; ラプラシアン; random walk; infinite particle system; stochastic numerical analysis; Laplacian on a graph; harmonic map; spectral structure; biharmonic operator; operator algebra; グラフの上のラプラシアン; 碓率数値解析; モンテカルロ解析; 無縁Brown粒子系; スペクトル; ラプラシアン

In this reseach project, Shimura considered asymptotic analysis for the exit probability of two dimensional random walk with drift from a quadrant, applying a technique from Monte Carlo Method. He examined applicability of some consequence from the theory of random walk defined on a Markov chain to the problem. Nishioka obtained "Ito calculus" and "Girsanov formula" for the biharmonic psudo process with the biharmnic operator as its generator. He also investigated some properties of solutions for a class of quasilinear biharmonic equations which is related with some problem from the fluid dynamics. Tanemuira considered precisely the uniqueness and the ergodicity for the infinite Brownian particle system with a hard core potential. Kotani obtained an asymptotic formula for the transition probability of a random walk on some infinite graphs. She also considered the spectral structure of some harmonic maps. Tsukada investigated the sufficiency for the statistics of some stochastic processes and infinite particle systems from the point of operator algebra. Ohguchi dealt with the numerical analysis of some Markov chains related to the finance, in which he examined usefulness of some quasi-random numbers.During the term of this project, the project members exchanged the related rescent results with M.Kondo (Shimane Univ.), K.Hirano (Osaka Univ.), T.Watanabe. (Okayama Science Univ.), M.Motoo (Tokyo Institute Technology), T.Yamada (Ritsumekan Univ.) and S.Sato (Tokyo Denki Univ.).

在这个研究项目中，Shimura考虑了渐近分析，用于从象限中漂移两维随机步行的退出概率，并应用了Monte Carlo方法的技术。他检查了马尔可夫链上定义的随机步行理论对问题的适用性。 Nishioka获得了Biharmonic Psudo工艺的“ ITO微积分”和“ Girsanov公式”，将Biharmnic操作员作为其发电机。他还研究了一类准线性双旋链方方程的溶液的某些特性，这与流体动力学中的一些问题有关。 Tanemuira精确地考虑了具有坚硬核心潜力的无限棕色粒子系统的独特性和牙齿性。 Kotani获得了在某些无限图上随机行走的过渡概率的渐近公式。她还考虑了一些谐波图的光谱结构。 Tsukada从操作员代数点研究了一些随机过程和无限粒子系统的统计数据。 Ohguchi处理了与金融有关的一些马尔可夫链的数值分析，他在其中检查了一些准随机数字的有用性。在该项目的术语中，项目成员与M.Kondo（Shimane Univ。），K.Hirano（Osaka Univ。 （冈山科学大学），M.Motoo（东京研究所技术），T.Yamada（Ritsumekan Univ。）和S.Sato（Tokyo Denki Univ。）。