Stochastic ranking process and function valued complete uniform law of large numbers

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03344
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Keio University
• Principal Investigator: HATTORI Tetsuya 慶應義塾大学, 経済学部(日吉), 教授 (10180902)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 確率論 / 数理科学 / 確率過程論 / 大数の法則 / 流体力学極限 / 数理統計学 / 確率順位付け模型

Outline of Final Research Achievements

We completed and published a paper on existence of hydrodynamic limits and propagation of chaos of the stochastic ranking processes, generalized to the cases of spatially dependent intensities for the point processes which determine the move-to-front (jump-to-top) random times. We also published (1) a paper on a complete law of large numbers which gives a basic framework of the main theorem, (2) a professional textbook which contains an introduction to the less popular complete law of large numbers, together with open problems, and (3) a basic textbook on measure theory, intended partially as a guidance towardss the main mathematical interest of the research results.
As explained in the report of the previous KAKENHI project by the author, the stochastic ranking processes are the particle systems which model the rankings on the web, such as sales ranks of online bookstores, and the models give mathematical basis for the analysis of so called long-tail structure of online retails.

Free Research Field

数物系科学

Academic Significance and Societal Importance of the Research Achievements

急速な発達によって時代を特徴付けるに至った計算機とネットワーク環境によって，インターネット小売業のような大規模なアイテムの人気度の全順位がリアルタイムで更新される現象が可視化されオンライン中古市場のように経済的な意味を持つ時代に，実際のデータと現象から論理的中核の抽出に成功していたが，その中核たる数学的内容を将来にわたって検討および勉強できるように，学術論文，専門的教科書，基礎演習書を刊行することができた．