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

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.).

在本研究计划中，Shimura应用MonteCarlo方法中的一种技巧，考虑了具有象限漂移的二维随机游动的退出概率的渐近分析。他审查适用性的一些后果理论的随机游走定义的马尔可夫链的问题。Nishioka得到了以双调和算子为生成元的双调和psudo过程的“Ito演算”和“Girsanov公式”。他还研究了一类拟线性双调和方程解的一些性质，这类方程与流体动力学中的一些问题有关。Tanemuira精确地考虑了具有硬核势的无限布朗粒子系统的唯一性和遍历性。Kotani得到了无限图上随机游动转移概率的一个渐近公式。她还考虑了一些调和映射的谱结构。Tsukada从算子代数的角度研究了某些随机过程和无穷粒子系统统计量的充分性。Ohguchi研究了与金融相关的马尔可夫链的数值分析，其中他检验了一些准随机数的有用性。在本项目期间，项目成员与M.Kondo（岛根大学）交换了相关的数值分析结果。K.Hirano（大坂大学），T.Watanabe.（冈山理科大学），M.Motoo（东京理工大学）、T.Yamada（立命馆大学）和S.Sato（Tokyo Denki Univ.）。

项目成果

塚田真(高橋眞映との共著): "The best possibility of the bound for the kantorovich inequality and some remarks" J.of Ivequalities and Applications. 1. 327-334 (1997)

Makoto Tsukada（与 Maye Takahashi 合着）：“坎托罗维奇不等式的界限的最佳可能性和一些评论”J.of Ivequalities and Applications (1997)。

塚田 真: "Imtevacting systems and sufficienoy" Proc.China and Japan Joint Symp.on Applied Math.(1999)

Makoto Tsukada：“Imtevacting systems and sufficienoy”Proc.China and Japan Joint Symp.on Applied Math.(1999)

西岡國雄: "The first hitting time and place of a halfline by a biharmonic pseudo process" Japan.J.of Mathematics. 23. 235-280 (1997)

Kunio Nishioka：“通过双调和伪过程的半线的第一次击球时间和地点”Japan.J.of Mathematics. 23. 235-280 (1997)

Tsukada, M.and Takahasi, S.-E.: "The best possi-bility of the bound for the Kantorovich inequaility and some remarks." J.Inequal.Appl.Vol.1. 327-334 (1997)

Tsukada, M. 和 Takahasi, S.-E.：“Kantorovich 不等式的界限的最佳可能性和一些评论。”

志村道夫: "Exit probabi lity of two-dimensional raudomwalk from the quadrasst" Proc.Japan Acad.75,SerA. 39-42 (1999)

Michio Shimura：“来自四边形的二维随机游走的退出概率”Proc.Japan Acad.75，SerA 39-42 (1999)。