{"title":"On A Family of Isospectral Pure-Birth Processes","authors":"L. Miclo, Chi Zhang","doi":"10.30757/alea.v18-65","DOIUrl":null,"url":null,"abstract":"The investigation of the spectra of finite Markov generators was first motivated by the quest of quantitative bounds on the convergence to equilibrium of the corresponding processes, see for instance the reference book Levin et al. (2009). There is also a classification reason: what are the possible spectra of Markov generators?, and for such a given spectrum, is there a simple representative Markov process? This structural question is related to the previous motivation, as ergodic finite isospectral Markov generators can be intertwined and under certain circumstances this relation enables good transfers of information about the speed of convergence, see e.g. Miclo (2018); Miclo and Patie (2021). Our goal here goes in this general direction, by providing a simple family of Markov generators for real spectra with geometric multiplicity 1.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","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.v18-65","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
The investigation of the spectra of finite Markov generators was first motivated by the quest of quantitative bounds on the convergence to equilibrium of the corresponding processes, see for instance the reference book Levin et al. (2009). There is also a classification reason: what are the possible spectra of Markov generators?, and for such a given spectrum, is there a simple representative Markov process? This structural question is related to the previous motivation, as ergodic finite isospectral Markov generators can be intertwined and under certain circumstances this relation enables good transfers of information about the speed of convergence, see e.g. Miclo (2018); Miclo and Patie (2021). Our goal here goes in this general direction, by providing a simple family of Markov generators for real spectra with geometric multiplicity 1.
对有限马尔可夫生成器谱的研究最初是由对相应过程收敛到平衡的定量界限的探索所激发的,例如参见参考书Levin et al.(2009)。还有一个分类原因:马尔可夫发生器的可能谱是什么?,对于这样一个给定的频谱,是否存在一个简单的具有代表性的马尔可夫过程?这个结构问题与前面的动机有关,因为遍历有限等谱马尔可夫生成器可以交织在一起,并且在某些情况下,这种关系能够很好地传递关于收敛速度的信息,例如Miclo (2018);Miclo and Patie(2021)。我们的目标是沿着这个大致的方向,通过提供一组简单的马尔可夫发生器,用于具有几何多重性1的实谱。
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.