Discrete random process stabilization

Abstract

In this paper the problem of automaton transformation of a discrete random process into the discrete random distribution (1/n, 1/n,…, 1/n) with any arbitrarily given accuracy is investigated. It is supposed that the properties of these input processes are not completely known, i.e., they are generated by an unstable random signal source. A class of “extremally” unstable random signal sources for which the generated random processes can still be transformed into the distribution (1/n, 1/n,…, 1/n) by an adder modulo n is introduced. An estimate of the distance between the obtained and the discrete uniform random distributions is also found, dependent on the number of operating steps of the adder, in the case when the input process is described by a finite Markov chain.