Journal of Applied Probability

On a 'replicating character string' model

Richard C. Bradley

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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.

Article information

Source
J. Appl. Probab., Volume 51, Number 2 (2014), 512-527.

Dates
First available in Project Euclid: 12 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1402578640

Digital Object Identifier
doi:10.1239/jap/1402578640

Mathematical Reviews number (MathSciNet)
MR3217782

Zentralblatt MATH identifier
1296.60086

Subjects
Primary: 60G10: Stationary processes

Keywords
Replicating character string stationarity absolute regularity

Citation

Bradley, Richard C. On a 'replicating character string' model. J. Appl. Probab. 51 (2014), no. 2, 512--527. doi:10.1239/jap/1402578640. https://projecteuclid.org/euclid.jap/1402578640


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