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On a ‘Replicating Character String’ Model

Part of: Stochastic processes

Published online by Cambridge University Press:  19 February 2016

Richard C. Bradley
Richard C. Bradley*
Affiliation:
Indiana University
*
∗ Postal address: Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA. Email address: bradleyr@indiana.edu.
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Abstract

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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.

Keywords

Replicating character stringstationarityabsolute regularity

MSC classification

Primary: 60G10: Stationary processes
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 512 - 527
Copyright
© Applied Probability Trust 

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