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.

首席研究员已经成功地将对称扩散的随机演算与不同国家的研究人员一起应用于不同的主题，并且结果已在三个国际期刊上发表。首席研究员与研究人员合作开发具有压缩p范数的一般函数空间的潜在理论，并将其应用于d集上的Besov空间和相关的跳跃型马尔可夫过程的研究。进一步，对于一般对称马尔可夫过程，证明了测度的容性等周不等式等价于测度支持下时变过程的超收缩性。研究结果以三篇论文的形式发表在国际期刊上。

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。