Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics

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    STOCHASTIC GAMES ON MARKOV PROCESSES WITH FINAL SEQUENCE OF STATES
    (Institutul de Matematică şi Informatică al AŞM, 2017) Lazari, Alexandru
    In this paper a class of stochastic games, defined on Markov processes with final sequence of states, is investigated. In these games each player, knowing the initial distribution of the states, defines his stationary strategy, represented by one proper transition matrix. The game is started by first player and, at every discrete moment of time, the stochastic system passes to the next state according to the strategy of the current player. After the last player, the first player acts on the system evolution and the game continues in this way until, for the first time, the given final sequence of states is achieved. The player who acts the last on the system evolution is considered the winner of the game. In this paper we prove that the distribution of the game duration is a homogeneous linear recurrence and we determine the initial state and the generating vector of this recurrence. Based on these results, we develop polynomial algorithms for determining the main probabilistic characteristics of the game duration and the win probabilities of players. Also, using the signomial and geometric programming approaches, the optimal cooperative strategies that minimize the expectation of the game duration are determined.
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    OPTIMIZATION OF MARKOV PROCESSES WITH FINAL SEQUENCE OF STATES AND UNITARY TRANSITION TIME
    (Valines SRL, 2014) Lazari, Alexandru
    In this paper the Markov processes with final sequence of states and unitary transition time are studied. These stochastic systems represent a generalization of zero-order Markov processes studied in [1]. The evolution time of these systems, as a function of distribution of the states and transit matrix, is minimized using signomial and geometric programming approaches.