{"title":"Spectral analysis of bilateral birth–death processes: some new explicit examples","authors":"Manuel D. de la Iglesia","doi":"10.1017/apr.2021.64","DOIUrl":null,"url":null,"abstract":"Abstract We consider the spectral analysis of several examples of bilateral birth–death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, such as recurrence, the invariant distribution (if it exists), and the probability current.","PeriodicalId":53160,"journal":{"name":"Advances in Applied Probability","volume":"54 1","pages":"1193 - 1221"},"PeriodicalIF":0.9000,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/apr.2021.64","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract We consider the spectral analysis of several examples of bilateral birth–death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, such as recurrence, the invariant distribution (if it exists), and the probability current.
期刊介绍：
The Advances in Applied Probability has been published by the Applied Probability Trust for over four decades, and is a companion publication to the Journal of Applied Probability. It contains mathematical and scientific papers of interest to applied probabilists, with emphasis on applications in a broad spectrum of disciplines, including the biosciences, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used.
A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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