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2019 Cancellation of fluctuation in stochastic ranking process with space-time dependent intensities
Tetsuya Hattori
Tohoku Math. J. (2) 71(3): 359-396 (2019). DOI: 10.2748/tmj/1568772177

Abstract

We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic distribution in the infinite particle limit. We assume topology of weak convergence for the space of distributions, which implies that the fluctuations among particles with different jump rates cancel in the limit. The results are proved by first finding an auxiliary stochastic ranking process, for which a strong law of large numbers is applied, and then applying a multi time recursive Gronwall's inequality. The limit has a representation in terms of non-Markovian processes which we call point processes with last-arrival-time dependent intensities. We also prove the propagation of chaos, i.e., the tagged particle processes also converge almost surely.

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Tetsuya Hattori. "Cancellation of fluctuation in stochastic ranking process with space-time dependent intensities." Tohoku Math. J. (2) 71 (3) 359 - 396, 2019. https://doi.org/10.2748/tmj/1568772177

Information

Published: 2019
First available in Project Euclid: 18 September 2019

zbMATH: 07155349
MathSciNet: MR4012354
Digital Object Identifier: 10.2748/tmj/1568772177

Subjects:
Primary: 60K35
Secondary: 82C22

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 3 • 2019
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