Stochastic analysis of infinite particle systems in nonequilibruim

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540122
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Chiba University
• Principal Investigator: TANEMURA Hideki 千葉大学, 理学(系)研究科(研究院), 教授 (40217162)
• Co-Investigator(Renkei-kenkyūsha): KATORI Makoto 中央大学, 理工学部, 教授 (60202016) ; SASAMOTO Tomohiro 東京工業大学, 大学院理工学研究科, 准教授 (70332640)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 行列式過程 / 確率微分方程式 / ダイソン模型 / エアリー過程 / ランダム行列 / ディリクレ形式 / 末尾シグマ加法族 / 非平衡系

Outline of Final Research Achievements

We study existence and uniqueness of infinite dimensional stochastic differential equations (ISDEs). We clarified the relation between the uniqueness of solutions and the triviality of tail sigma fields. Applying the result, we obtained the uniqueness of strong solutions of ISDEs describing the systems of Brownian motions with long range interaction including logarithmic potential, and determined the Dirichlet forms associated with the systems.

Free Research Field

確率論