Studies on diffusion processes and fuzzy valued stochastic analysis

扩散过程和模糊值随机分析的研究

• 批准号: 19540140
• 负责人: OGURA Yukio
• 金额: $ 2.66万
• 依托单位: Saga University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540140/
• 关键词: 拡散過程; マルコフ性; ファジィ集合値確率変数; 集合係数の確率微分方程式; 大偏差原理; Chern-Simons理論; Poisson-Dirichlet分布; 中偏差原理; Chern-Simon摂動展開理論; 集合値関数の確率積分; 大数の強法則; Chern-Simons汎関数; 確率微分方程式の比較定理

In this study, we first found a lot of new type of stochastic processes in the class of one-dimensional continuous stochastic process with Markov property but without strong Markov property, and moreover determined that class. We then extended strong laws of large numbers and derived large deviation principle for fuzzy set valued random variables. In addition, we proved the existence and uniqueness of solutions almost surely in the space of fuzzy sets (resp. sets) to stochastic differential equations with fuzzy sets (resp. sets) coefficients. We also estimated the term with power 3 integrand in the asymptotic expansion in perturbative Chern-Simons theory. A new characterization of the two-parameter Poisson-Dirichlet distribution was given.

在这项研究中，我们首先在一维连续随机过程类中发现了许多新的随机过程，并且确定了这类过程。然后推广了强大数定律，导出了模糊集值随机变量的大偏差原理。此外，我们还证明了在模糊集空间中解的存在唯一性。集)转化为具有模糊集的随机微分方程组。集合)系数。我们还估计了微扰Chern-Simons理论渐近展开式中的3次方被积项。给出了双参数Poisson-Dirichlet分布的一个新的刻画。

项目成果

Asymptotic expansion of perturbative Chern-Simons theory via Wiener space

微扰陈-西蒙斯理论通过维纳空间的渐近展开

• 发表时间: 2009
• 期刊: Bull. Sci. Math. 133
• 作者: Sergio Albeverio;Itaru Mitoma
• 通讯作者: Itaru Mitoma

2パラメータPoisson-Dirichlet点過程

2 参数泊松-狄利克雷点过程

• 发表时间: 2007
• 作者: Iacus;S. M;et al.;半田 賢司
• 通讯作者: 半田 賢司

Large and Moderate Deviations of Random Upper Semicontinuous Functions

随机上半连续函数的大偏差和中偏差

• DOI: 10.1080/07362990903136470
• 发表时间: 2010-02
• 期刊: Stochastic Analysis and Applications
• 影响因子: 1.3
• 作者: Xia Wang;Shoumei Li;Yukio Ogura
• 通讯作者: Yukio Ogura

A remark on stochastic differential equations with set coefficients

关于带集合系数的随机微分方程的评述

• 发表时间: 2007
• 作者: Uchida;M.;Yukio Ogura
• 通讯作者: Yukio Ogura

On some metrics compatible with the Fell-Matheron topology

• DOI: 10.1016/j.ijar.2006.12.008
• 发表时间: 2007-09
• 期刊: Int. J. Approx. Reason.
• 作者: Y. Ogura