Time-series data analysis methods for small systems based on algebraic probability theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 25870339
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Biological physics/Chemical physics/Soft matter physics; Soft computing
• Research Institution: Saitama University (2015); Kyoto University (2013-2014)
• Principal Investigator: OHKUBO Jun 埼玉大学, 理工学研究科, 准教授 (70451888)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 確率過程 / 出生死滅過程 / 化学反応系 / 非可換代数 / Doi-Peliti法 / 時系列データ解析

Outline of Final Research Achievements

Doi-Peliti formalism has been mainly used to analyze birth-death processes, which deals with discrete state variables. I investigated the mathematical meanings of the formalism, and it has been found that discrete variables can be connected to continuous variables and their differentials via the Doi-Peliti formalism. Using the findings, it is possible to derive dual processes from the original stochastic processes in systematic ways. Applying the duality concepts, dual processes for some stochastic differential equations and birth-death processes have been derived. In addition, using the dual processes, it is possible to construct rapid computational frameworks for time-series data analysis for the original stochastic processes.

Free Research Field

数理工学，統計的機械学習，情報統計力学，確率過程の数理とその応用