Geodesic
Determining the distribution of the duration of stationary games for zero-order markov processes with final sequence of states
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2015), pp. 72-78.

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A zero-order Markov process with final sequence of states represents a stochastic system with independent transitions that stops its evolution as soon as given final sequence of states is reached. The transition time of the system is unitary and the transition probability depends only on the destination state. We consider the following game. Initially, each player defines his distribution of the states. The initial distribution of the states is established according to the distribution given by the first player. After that, the stochastic system passes consecutively to the next state according to the distribution given by the next player. After the last player, the first player acts on the system evolution and the game continues in this way until the given final sequence of states is achieved. Our goal is to study the duration of this game, knowing the distribution established by each player and the final sequence of states of the stochastic system. It is proved that the distribution of the duration of the game is a homogeneous linear recurrent sequence and it is developed a polynomial algorithm to determine the initial state and the generating vector of this recurrence. Using the generating function, the main probabilistic characteristics are determined. 
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Alexandru Lazari. Determining the distribution of the duration of stationary games for zero-order markov processes with final sequence of states. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2015), pp. 72-78. http://geodesic.mathdoc.fr/item/BASM_2015_3_a5/

[1] Lazari A., Lozovanu D., Capcelea M., Dynamical deterministic and stochastic systems: Evolution, optimization and discrete optimal control, CEP USM, Chişinău, 2015, 310 pp. (in Romanian)

[2] Lazari A., “Determining the Optimal Evolution Time for Markov Processes with Final Sequence of States”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2015, no. 1(77), 115–126 | MR

[3] Lazari A., “Evolution Time of Composed Stochastic Systems with Final Sequence of States and Independent Transitions”, Annals of the Alexandru Ioan Cuza University – Mathematics, December 2014, 18 pp., ISSN (Online) 1221-8421 | DOI

[4] Lazari A., “Optimization of Zero-Order Markov Processes with Final Sequence of States”, Universal Journal of Applied Mathematics (Horizon Research Publishing), 1:3 (2013), 198–206

[5] Lazari A., “Compositions of stochastic systems with final sequence states and interdependent transitions”, Annals of the University of Bucharest, 4(LXII):1 (2013), 289–303 | MR | Zbl

[6] Lazari A., “Algorithms for Determining the Transient and Differential Matrices in Finite Markov Processes.”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 2010, no. 2(63), 84–99 | MR | Zbl

[7] Zbaganu G., “Waiting for an ape to type a poem”, Bul. Acad. Ştiinţe Repub. Moldova, Mat., 1992, no. 2(8), 66–74 | MR | Zbl

[8] Guibas Leo J., Odlyzko Andrew M., “Periods in Strings”, Journal of Combinatorial Theory, Series A, 30 (1981), 19–42 | DOI | MR | Zbl