Stochastic ranking process with space-time dependent intensities

Tetsuya Hattori, Seiichiro Kusuoka

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic distribution, and also the tagged particle processes converge almost surely, in the infinite particle limit. The limit distribution is characterized by a system of inviscid Burgers-like integral-partial differential equations with evaporation terms, and the limit process of a tagged particle is a motion along a characteristic curve of the differential equations except at its Poisson timesof jumps to the origin.

Original languageEnglish
Pages (from-to)571-607
Number of pages37
JournalAlea
Volume9
Issue number2
Publication statusPublished - 2012

Fingerprint

Ranking
Space-time
Tagged Particle
Jump
Dependent
Converge
Characteristic Curve
Empirical Distribution
Limit Distribution
Evaporation
Joint Distribution
Siméon Denis Poisson
Partial differential equation
Differential equation
Motion
Term
Model

Keywords

  • Hydrodynamic limit
  • Inviscid Burgers equation
  • Move-to-front rules.
  • Poisson process
  • Stochastic ranking process

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Stochastic ranking process with space-time dependent intensities. / Hattori, Tetsuya; Kusuoka, Seiichiro.

In: Alea, Vol. 9, No. 2, 2012, p. 571-607.

Research output: Contribution to journalArticle

Hattori, T & Kusuoka, S 2012, 'Stochastic ranking process with space-time dependent intensities', Alea, vol. 9, no. 2, pp. 571-607.
Hattori, Tetsuya ; Kusuoka, Seiichiro. / Stochastic ranking process with space-time dependent intensities. In: Alea. 2012 ; Vol. 9, No. 2. pp. 571-607.
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