研究者情報 | 神奈川大学

ヨシダ　ミノル Yoshida Minoru 吉田　稔所属神奈川大学情報学部システム数理学科神奈川大学大学院工学研究科工学専攻（情報システム創成領域）職種教授
言語種別	英語
発行・発表の年月	2021/08
形態種別	学術雑誌
査読	査読あり
標題	Non-local Markovian symmetric forms on infinite dimensional spaces (1: closability and the quasi regularlity)
執筆形態	共著
掲載誌名	Communications in Mathematical Phyisics
掲載区分	国外
出版社・発行元	Springer-Verlag
巻・号・頁	388,pp.659-706
著者・共著者	Sergio Albeverio et. al.
概要	General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $(S, {\cal B}(S), \mu)$, with $S$ Fr{\'e}chet spaces such that $S \subset {\mathbb R}^{\mathbb N}$, ${\cal B}(S)$ is the Borel $\sigma$-field of $S$, and $\mu$ is a Borel probability measure on $S$, are introduced.Firstly, a family of non-local Markovian symmetric forms ${\cal E}_{(\alpha)}$, $0 < \alpha < 2$, acting in each given $L^2(S; \mu)$ is defined, the index $\alpha$ characterizing the order of the non-locality.Then, it is shown that all the forms ${\cal E}_{(\alpha)}$ defined on $\bigcup_{n \in {\mathbb N}}C^{\infty}_0({\mathbb R}^n)$ are closable in $L^2(S;\mu)$. Moreover, sufficient conditions under which the closure of the closable forms, that are Dirichlet forms, become strictly quasi-regular, are given. Finally, an existence theorem for Hunt processes properly associated to the Dirichlet forms is given.