Study of local structures and noises of symmetric diffusion processes associated with Dirichlet forms

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540170
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka University (2013-2014); Kyoto University (2012)
• Principal Investigator: HINO Masanori 大阪大学, 基礎工学研究科, 教授 (40303888)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 確率解析 / Dirichlet形式 / 対称拡散過程 / 局所構造 / ノイズ / フラクタル / ウィナー空間 / エネルギー測度

Outline of Final Research Achievements

I studied local structures and noises of diffusion processes associated with Dirichlet forms on spaces with anomalous structures such as fractals and infinite dimensional spaces. In particular, I proved some relations between two distances on a class of fractals derived from natural Dirichlet forms, and studied a general theory and nontrivial examples of functions of locally bounded variations on the Wiener space together with their applications to stochastic analysis. The papers on these studies have been published in academic journals. Moreover, I wrote a survey paper based on my studies of the past several years.

Free Research Field

確率論