Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics

Permanent URI for this communityhttps://msuir.usm.md/handle/123456789/12

Browse

Author: search.filters.author.Lazari, Alexandru

Search Results

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    PROBABILITĂŢILE LIMITĂ DE TRANSFER ALE SISTEMELOR ALEATORII DISCRETE
    (CEP USM, 2009) Lazari, Alexandru
    In this article we study discrete random systems with finite set of states. A polynomial time algorithm for determining the limit matrix of probabilities in Markov processes is proposed and grounded.
  • Thumbnail Image
    Item
    CARACTERISTICILE PROBABILISTICE ALE TIMPULUI DE EVOLUŢIE AL SISTEMELOR ALEATOARE DISCRETE
    (CEP USM, 2009) Lazari, Alexandru
    In this article it is being studied a class of random discrete systems, developing polynomial algorithms for determining the basic characteristics of time evolution of their own. It is a generalized problem for the case when the transfer time of the system in the next state is also a random variable with known distribution law. The developed algorithms are based on probabilistic method of determining the characteristics of random variables, knowing the generating function or characteristic function of them. Algorithms are being presented for numerical derivation of functions composed and rational fractions that appear later in main algorithms. It makes a brief foray into the theory of homogeneous linear recurring series to argue theoretically developed algorithms.
  • Thumbnail Image
    Item
    ALGORITMI EFICIEN Ţ I PENTRU REZOLVAREA SISTEMELOR DE ECUAŢII CE APAR LA DISCRETIZAREA ECUAŢIILOR INTEGRALE SINGULARE
    (CEP USM, 2008) Capcelea, Maria; Capcelea, Titu; Lazari, Alexandru
    It is marked out the class of iterative algorithms for solvin g of systems of equations which are obtained when discre- tizing SIE with discontinuous coefficients. These algorithms permit essential reducing of computational cost for finding an approximate solution, at that not losing in the quality of other numerical characteristics - they are numerically stable and allow us to check precision in the course of iterations without calculation of approximation of a solution.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    DETERMINING THE OPTIMAL EVOLUTION TIME FOR MARKOV PROCESSES WITH FINAL SEQUENCE OF STATES
    (Academy of Sciences of Moldova, 2015) Lazari, Alexandru
    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.