Stochastic ranking process with time dependent intensities

Yuu Hariya, Kumiko Hattori, Tetsuya Hattori, Yukio Nagahata, Yuusuke Takeshima, Takahisa Kobayashi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the infinite particle limit. We give an explicit formula for the limit distribution and show that the limit distribution function is a unique global classical solution to an initial value problem for a system of a first order non-linear partial differential equations with time dependent coefficients.

Original languageEnglish
Pages (from-to)77-111
Number of pages35
JournalTohoku Mathematical Journal
Volume63
Issue number1
DOIs
Publication statusPublished - 2011 Mar

Fingerprint

Limit Distribution
Ranking
Poisson Random Measure
Global Classical Solution
Empirical Distribution
Nonlinear Partial Differential Equations
Joint Distribution
Initial Value Problem
Explicit Formula
Distribution Function
Jump
First-order
Converge
Coefficient

Keywords

  • Hydrody-namic limit
  • Inviscid Burgers equation with evaporation
  • Least-recently-used caching
  • Move-to-front rules
  • Poisson random measure
  • Stochastic ranking process

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hariya, Y., Hattori, K., Hattori, T., Nagahata, Y., Takeshima, Y., & Kobayashi, T. (2011). Stochastic ranking process with time dependent intensities. Tohoku Mathematical Journal, 63(1), 77-111. https://doi.org/10.2748/tmj/1303219937

Stochastic ranking process with time dependent intensities. / Hariya, Yuu; Hattori, Kumiko; Hattori, Tetsuya; Nagahata, Yukio; Takeshima, Yuusuke; Kobayashi, Takahisa.

In: Tohoku Mathematical Journal, Vol. 63, No. 1, 03.2011, p. 77-111.

Research output: Contribution to journalArticle

Hariya, Y, Hattori, K, Hattori, T, Nagahata, Y, Takeshima, Y & Kobayashi, T 2011, 'Stochastic ranking process with time dependent intensities', Tohoku Mathematical Journal, vol. 63, no. 1, pp. 77-111. https://doi.org/10.2748/tmj/1303219937
Hariya, Yuu ; Hattori, Kumiko ; Hattori, Tetsuya ; Nagahata, Yukio ; Takeshima, Yuusuke ; Kobayashi, Takahisa. / Stochastic ranking process with time dependent intensities. In: Tohoku Mathematical Journal. 2011 ; Vol. 63, No. 1. pp. 77-111.
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