@article{AIHPB_2004__40_1_43_0, author = {Manita, A. and Simonot, F.}, title = {A note on the two-sided regulated random walk}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {40}, year = {2004}, pages = {43-52}, doi = {10.1016/j.anihpb.2003.06.002}, mrnumber = {2037472}, zbl = {1037.60083}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_1_43_0} }
Manita, A.; Simonot, F. A note on the two-sided regulated random walk. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) pp. 43-52. doi : 10.1016/j.anihpb.2003.06.002. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_1_43_0/
[1] Applied Probability and Queues, Wiley, 1987. | MR 889893 | Zbl 0624.60098
,[2] Asymptotic Methods in Queuing Theory, Wiley, 1984. | MR 745620 | Zbl 0544.60085
,[3] Monotone infinite stochastic matrices and their augmented truncations, Stochastic Process. Appl. 24 (1987) 287-292. | MR 893176 | Zbl 0623.60089
, ,[4] Brownian Motion and Stochastic Flow Systems, Krieger Publishing Company, Malabar, FL, 1990. | MR 1092214 | Zbl 0716.60092
,[5] Modeling and Analysis of Computer Communications Networks, Plenum Press, New York, 1984.
,[6] Limits of queues as the waiting room grows, QUESTA 5 (1989) 381-392. | MR 1030477 | Zbl 0684.60073
, ,[7] Approximating the stationary distribution of an infinite stochastic matrix, J. Appl. Probab. 28 (1991) 96-103. | MR 1090450 | Zbl 0721.60070
,[8] Mathematical Methods in Queuing Theory, Kluwer Academic, 1994. | MR 1319595 | Zbl 0836.60098
,[9] Boundary Problems for Compound Poisson Process, Naukova Dumka, Kiev, 1975. | MR 402939
,[10] Stochastic Models in Queueing Theory, Academic Press, 1991. | Zbl 0743.60100
,[11] Stochastic Storage Processes, Springer-Verlag, New York, 1980. | MR 602329 | Zbl 0453.60094
,[12] Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone, Stochastic Process. Appl. 56 (1995) 133-149. | MR 1324326 | Zbl 0820.60051
,[13] Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices, J. Appl. Probab. 33 (1996) 974-985. | MR 1416220 | Zbl 0867.60041
, ,[14] Moment based approximation for the stationary distribution of a random walk in Z+ with an application to the M/G/1/n queueing system, J. Appl. Probab. 37 (2000) 290-299. | MR 1761680 | Zbl 0959.60030
,[15] F. Simonot, A.D. Manita, Convergence time to equilibrium for nonhomogeneous stochastically monotone Markov chains, Preprint 9, Lyapounov French-Russian Institute, Moscow, 2001.
[16] Comparison Methods for Queues and Other Stochastic Models, Wiley, 1983. | MR 754339 | Zbl 0536.60085
,[17] Stochastic Modelling and Analysis, Wiley, 1986. | MR 847718
,[18] Truncation Approximations of Invariant Measures for Markov Chains, J. Appl. Probab. 35 (1998) 517-536. | MR 1659488 | Zbl 0919.60065
,[19] Approximation of the invariant probability distribution of an infinite stochastic matrix, Adv. Appl. Probab. 12 (1980) 710-726. | MR 578845 | Zbl 0443.60030
,