Stochastic Calculus for symmetric diffusion processes and its applications

对称扩散过程的随机微积分及其应用

• 批准号: 13640143
• 负责人: FUKUSHIMA Masatoshi
• 金额: $ 1.73万
• 依托单位: Kansai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640143/
• 关键词: symmetric diffusion; abstract Wiener space; stochastic stopping game; isoperimetric inequality; ultracontractivity; time changed process; d-set; Besov space; 対称マルコフ過程; 強容量不等式; 対称安定過程; α-集合; Wiener空間; BV関数; ディリクレ空間; ソボトフ不等式; 極集合; 正則部分空間

The head investigator has succeeded to apply the stochastic calculus of symmetric diffusions to different subjects with researchers in different countries, and the results have been published in three international journals. The head investigator collaborates with investigators to develop potential theory for a general function space with contractive p-norm and apply it to the study of Besov spaces on d-sets and associated jump type Markov processes. Furthermore, for a general symmetric Markov process, a capacitary isoperimetric inequality of a measure is shown to be equivalent to the ultracontractivity of the time changed process on the support of measure. The results are being published as three papers in international journals.

首席调查员已成功地将对称扩散的随机演算应用于不同国家的研究人员的不同受试者，结果已在三种国际期刊上发表。首席研究人员与研究人员合作，通过承包P-Norm为一般功能空间开发潜在的理论，并将其应用于D-SETS和相关的跳跃类型Markov过程的BESOV空间的研究。此外，对于一般的对称马尔可夫过程，量度的同类等等不平等现象被证明等于时间变化的过程在支持度量方面的超级缩写率。结果在国际期刊上以三篇论文的形式发表。

项目成果

M. Fukushima and T. Uemura: "On Sobolev and capacitary inequalities for contractive Besov spaces over d-sets"Potential Analysis. 18. 59-77 (2003)

M. Fukushima 和 T. Uemura：“关于 d 集上收缩贝索夫空间的 Sobolev 和电容不等式”潜在分析。

T.Uemura: "On some path properties of symmetric stable-like processes for one dimension"Potential Analysis. 16. 79-91 (2002)

T.Uemura：“关于一维对称稳定类过程的某些路径性质”的潜力分析。

M.Fukushima, M.Hino: "On the space of BV functions and a related stochastic calculus in infinite dimensions"J. Functional Analysis. 183. 245-261 (2001)

M.Fukushima，M.Hino：“关于 BV 函数的空间和相关的无限维随机微积分”J。

M.Fukushima, M.Hino: "On the space of BV functions and a related stochastic calculus in infinite dimensions"J.Functional Analysis. 183. 245-261 (2001)

M.Fukushima，M.Hino：“关于 BV 函数的空间和无限维中的相关随机微积分”J.Functional Analysis。

M. Fukushima and J. Ying: "A note on regular Dirichlet subspaces"Proc. Amer. Math. Soc.. 131. 1607-1610 (2003)

M. Fukushima 和 J. Ying：“关于正则狄利克雷子空间的注释”Proc。