June 2014 On a 'replicating character string' model
Richard C. Bradley
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J. Appl. Probab. 51(2): 512-527 (June 2014). DOI: 10.1239/jap/1402578640

Abstract

In Chaudhuri and Dasgupta's 2006 paper a certain stochastic model for 'replicating character strings' (such as in DNA sequences) was studied. In their model, a random 'input' sequence was subjected to random mutations, insertions, and deletions, resulting in a random 'output' 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 'input' sequence would be preserved by the 'output' sequence, and they proved a similar 'preservation' result for the property of strong mixing with exponential mixing rate. In our setup, we will in spirit slightly extend their 'preservation of stationarity' result, and also prove a 'preservation' result for the property of absolute regularity with summable mixing rate.

Citation

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Richard C. Bradley. "On a 'replicating character string' model." J. Appl. Probab. 51 (2) 512 - 527, June 2014. https://doi.org/10.1239/jap/1402578640

Information

Published: June 2014
First available in Project Euclid: 12 June 2014

zbMATH: 1296.60086
MathSciNet: MR3217782
Digital Object Identifier: 10.1239/jap/1402578640

Subjects:
Primary: 60G10

Keywords: absolute regularity , Replicating character string , stationarity

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 2 • June 2014
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