Tohoku Mathematical Journal
2011
March
SECOND SERIES VOL. 63, NO. 1

Tohoku Math. J.
63 (2011), 77-111

Title STOCHASTIC RANKING PROCESS WITH TIME DEPENDENT INTENSITIES

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

(Received May 26, 2010, revised October 13, 2010)
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.

2000 Mathematics Subject Classification. Primary 60K35; Secondary 35C05, 82C22.
Key words and phrases. Stochastic ranking process, move-to-front rules, least-recently-used caching, hydrodynamic limit, inviscid Burgers equation with evaporation, Poisson random measure.

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