Existence of an infinite particle limit of stochastic ranking process

Kumiko Hattori, Tetsuya Hattori

研究成果: Article査読

8 被引用数 (Scopus)

抄録

We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon.co.jp). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the queue, and otherwise stays in the queue, being pushed toward the tail every time another particle jumps to the top. In an infinite particle limit, the random motion of each particle between its jumps converges to a deterministic trajectory. (This trajectory is actually observed in the ranking data on web sites.) We prove that the (random) empirical distribution of this particle system converges to a deterministic space-time-dependent distribution. A core of the proof is the law of large numbers for dependent random variables.

本文言語English
ページ(範囲)966-979
ページ数14
ジャーナルStochastic Processes and their Applications
119
3
DOI
出版ステータスPublished - 2009 3月
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • モデリングとシミュレーション
  • 応用数学

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