Abstract:
This paper describes a class of dynamical stochastic systems that represents 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 ofprocesses represents a generalization 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 besolved using the signomial and geometric programming approaches.
