Study of bi-generalized diffusion processes by means of limits of generalized diffusion processes

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400139
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nara Women's University
• Principal Investigator: Tomisaki Matsuyo 奈良女子大学, 名誉教授 (50093977)
• Co-Investigator(Kenkyū-buntansha): TAKEMURA Tomoko 奈良女子大学, 研究院自然科学系, 助教 (40598140) ; IIZUKA Masaru 九州歯科大学, 歯学部, 准教授 (20202830)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 広義拡散過程 / 双一般化拡散過程 / 極限定理 / 正値連続加法的汎関数 / 局所時間 / モランモデル

Outline of Final Research Achievements

We considered properties of bi-generalized diffusion processes which are limits of generalized diffusion processes. We showed that weak mutation limits of the Moran model cannot be weak convergence limits in the space of cadlag functions, though they satisfy the strong Markov property. In the case that the limit of sequence of scale functions and that of speed measure functions have common discontinuous points, we showed that there exists a limit process whose state space has no topological structure. This result indicates that it is necessary to consider properties of bi-generalized diffusion processes by means of limit distributions instead of topological structure of state space.

Free Research Field

数物系科学