Stochastic ranking process with time dependent intensities

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

doi:10.2748/tmj/1303219937

Stochastic ranking process with time dependent intensities

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

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	77-111
Number of pages	35
Journal	Tohoku Mathematical Journal
Volume	63
Issue number	1
DOIs	https://doi.org/10.2748/tmj/1303219937
Publication status	Published - 2011 Mar
Externally published	Yes

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)

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10.2748/tmj/1303219937

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title = "Stochastic ranking process with time dependent intensities",

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.",

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

author = "Yuu Hariya and Kumiko Hattori and Tetsuya Hattori and Yukio Nagahata and Yuusuke Takeshima and Takahisa Kobayashi",

year = "2011",

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language = "English",

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AU - Hariya, Yuu

AU - Hattori, Kumiko

AU - Hattori, Tetsuya

AU - Nagahata, Yukio

AU - Takeshima, Yuusuke

AU - Kobayashi, Takahisa

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - Hydrody-namic limit

KW - Inviscid Burgers equation with evaporation

KW - Least-recently-used caching

KW - Move-to-front rules

KW - Poisson random measure

KW - Stochastic ranking process

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JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

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Stochastic ranking process with time dependent intensities

Abstract

Keywords

ASJC Scopus subject areas

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