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- Title
Functional central limit theorem for tagged particle dynamics in stochastic ranking process with space-time dependent intensities.
- Authors
Yukio Nagahata
- Abstract
In this paper, we consider a "parabolic" scaling limit of tagged particle dynamics and that of empirical measure of the position of particles for stochastic ranking process with space-time dependent intensities. A stochastic ranking process is driven according to an algorithm for a self-organizing linear list of a finite number of items. We regard this process as a particle system. We fasten a tag to a "particle" (item) and observe the (normalized) motion of the "tagged particle". We obtain a sum of diffusion processes between each two successive jump time for a "parabolic" scaling limit of tagged particle dynamics. In order to obtain the diffusion process, we have to observe a "parabolic" scaling limit of empirical measure of the position of particles. We also obtain a generalized Ornstein-Uhlenbeck process for a "parabolic" scaling limit of empirical measure of the position of particles.
- Subjects
CENTRAL limit theorem; STOCHASTIC processes; DIFFUSION processes; ORNSTEIN-Uhlenbeck process; PARTICLE dynamics analysis
- Publication
ALEA. Latin American Journal of Probability & Mathematical Statistics, 2022, Vol 19, Issue 1, p1001
- ISSN
1980-0436
- Publication type
Article
- DOI
10.30757/ALEA.v19-40