{"title":"时空相关随机排序过程中标记粒子动力学的泛函中心极限定理","authors":"Yukio Nagahata","doi":"10.30757/alea.v19-40","DOIUrl":null,"url":null,"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.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Functional central limit theorem for tagged particle dynamics in stochastic ranking process with space-time dependent intensities\",\"authors\":\"Yukio Nagahata\",\"doi\":\"10.30757/alea.v19-40\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":49244,\"journal\":{\"name\":\"Alea-Latin American Journal of Probability and Mathematical Statistics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Alea-Latin American Journal of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.30757/alea.v19-40\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Alea-Latin American Journal of Probability and Mathematical Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.30757/alea.v19-40","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Functional central limit theorem for tagged particle dynamics in stochastic ranking process with space-time dependent intensities
. 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.
期刊介绍:
ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted.
ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper.
ALEA is affiliated with the Institute of Mathematical Statistics.