FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 4, PAGES 1029-1043

Transient dynamics of two interacting random strings

A. A. Zamyatin
A. A. Yambartsev

Abstract

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A finite string is just a sequence of symbols from finite alphabet. We consider a Markov chain with the state space equal to the set of all pairs of strings. Transition probabilities depend only on d leftmost symbols in each string. Besides that, the jumps of the chain are bounded: the lengths of strings at subsequent moments of time cannot differ by more than some d.

We consider the case when dynamics of Markov chain is transient, i.e. as t → ¥ the lengths of both strings tend to infinity with probability 1. In this situation we prove stabilization law: the distribution of symbols close to left ends of strings tends to those of some random process.

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