**Authors:** Alexandru Lazari

### Abstract

This paper describes a class of dynamical stochastic
systems that re\-pre\-sents an extension of classical Markov
decision processes. The Markov stochastic systems with given final
sequence of states and unitary transition time, over a finite or
infinite state space, are studied. Such dynamical system stops its
evolution as soon as given sequence of states in given order is
reached. The evolution time of the stochastic system with fixed
final sequence of states depends on initial distribution of the
states and probability transition matrix. The considered class of
processes represents a ge\-ne\-ra\-li\-za\-tion of zero-order
Markov processes, studied in [3]. We are seeking for the
optimal initial distribution and optimal probability transition
matrix that provide the minimal evolution time for the dynamical
system. We show that this problem can be solved using the
signomial and geometric programming approaches.

Moldova State University

60 Mateevici str., Chișinău

Republic of Moldova, MD−2009

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