Stochastic ranking processes and their applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540147
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: HATTORI KUMIKO 首都大学東京, 理工学研究科, 教授 (80231520)
• Co-Investigator(Renkei-kenkyūsha): HATTORI Tetsuya 慶應義塾大学, 経済学部, 教授 (10180902)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 確率過程 / 極限定理 / 非マルコフ過程 / ループ・イレーズド・ランダム・ウォーク / 連続極限 / 確率ランキングモデル / ロングテール

Outline of Final Research Achievements

We constructed a stochastic ranking process with jump times determined by Poisson random measures and studied its infinite particle limit. The limit distribution of the scaled position and the intensity converges almost surely and the distribution function is related to a system of non-linear partial differential equations. This process has application to the sales ranks of an online bookstore, where the sales rate of each book varies with time. /We found a new method to construct a loop-erased random walk on the finite pre-Sierpinski gasket. We proved the existence of the scaling limit and obtained some sample path properties of the limit process. This method is applicable to various sorts of random walks and allows us to obtain a new family of self-avoiding walks.

Free Research Field

数物系科学