{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:47:50Z","timestamp":1740491270986,"version":"3.38.0"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>In Chaudhuri and Dasgupta's 2006 paper a certain stochastic model for \u2018replicating character strings\u2019 (such as in DNA sequences) was studied. In their model, a random \u2018input\u2019 sequence was subjected to random mutations, insertions, and deletions, resulting in a random \u2018output\u2019 sequence. In this paper their model will be set up in a slightly different way, in an effort to facilitate further development of the theory for their model. In their 2006 paper, Chaudhuri and Dasgupta showed that, under certain conditions, strict stationarity of the \u2018input\u2019 sequence would be preserved by the \u2018output\u2019 sequence, and they proved a similar \u2018preservation\u2019 result for the property of strong mixing with exponential mixing rate. In our setup, we will in spirit slightly extend their \u2018preservation of stationarity\u2019 result, and also prove a \u2018preservation\u2019 result for the property of absolute regularity with summable mixing rate.<\/jats:p>","DOI":"10.1017\/s0021900200011396","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:51:10Z","timestamp":1459248670000},"page":"512-527","source":"Crossref","is-referenced-by-count":0,"title":["On a \u2018Replicating Character String\u2019 Model"],"prefix":"10.1017","volume":"51","author":[{"given":"Richard C.","family":"Bradley","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"volume-title":"Introduction to Computational Biology","year":"1995","key":"S0021900200011396_ref19"},{"volume-title":"Random Walks with Stationary Increments and Renewal Theory","year":"1979","key":"S0021900200011396_ref1"},{"key":"S0021900200011396_ref17","first-page":"628","volume":"21","year":"1976","journal-title":"Theory Prob. 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