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

View as HTML     View as gif image

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 $t\; \to$¥ 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.

Location: http://mech.math.msu.su/~fpm/eng/96/964/96405h.htm
Last modified: March 19, 2005