A note on the two-sided regulated random walk
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 1, pp. 43-52.
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     title = {A note on the two-sided regulated random walk},
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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) no. 1, pp. 43-52. doi : 10.1016/j.anihpb.2003.06.002. http://www.numdam.org/articles/10.1016/j.anihpb.2003.06.002/

[1] S. Asmussen, Applied Probability and Queues, Wiley, 1987. | MR | Zbl

[2] A.A. Borovkov, Asymptotic Methods in Queuing Theory, Wiley, 1984. | MR | Zbl

[3] D. Gibson, E. Seneta, Monotone infinite stochastic matrices and their augmented truncations, Stochastic Process. Appl. 24 (1987) 287-292. | MR | Zbl

[4] J.M. Harrison, Brownian Motion and Stochastic Flow Systems, Krieger Publishing Company, Malabar, FL, 1990. | MR | Zbl

[5] J.F. Hayes, Modeling and Analysis of Computer Communications Networks, Plenum Press, New York, 1984.

[6] D.P. Heyman, W. Whitt, Limits of queues as the waiting room grows, QUESTA 5 (1989) 381-392. | MR | Zbl

[7] D.P. Heyman, Approximating the stationary distribution of an infinite stochastic matrix, J. Appl. Probab. 28 (1991) 96-103. | MR | Zbl

[8] V.V. Kalashnikov, Mathematical Methods in Queuing Theory, Kluwer Academic, 1994. | MR | Zbl

[9] V.S. Korolyuk, Boundary Problems for Compound Poisson Process, Naukova Dumka, Kiev, 1975. | MR

[10] J. Mehdi, Stochastic Models in Queueing Theory, Academic Press, 1991. | Zbl

[11] N.U. Prabhu, Stochastic Storage Processes, Springer-Verlag, New York, 1980. | MR | Zbl

[12] F. Simonot, Sur l'approximation de la distribution stationnaire d'une chaîne de Markov stochastiquement monotone, Stochastic Process. Appl. 56 (1995) 133-149. | MR | Zbl

[13] F. Simonot, Y.Q. Song, Characterization of convergence rates for the approximation of the stationary distribution of infinite monotone stochastic matrices, J. Appl. Probab. 33 (1996) 974-985. | MR | Zbl

[14] F. Simonot, 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 | Zbl

[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] D. Stoyan, Comparison Methods for Queues and Other Stochastic Models, Wiley, 1983. | MR | Zbl

[17] H.C. Tijms, Stochastic Modelling and Analysis, Wiley, 1986. | MR

[18] R.L. Tweedie, Truncation Approximations of Invariant Measures for Markov Chains, J. Appl. Probab. 35 (1998) 517-536. | MR | Zbl

[19] D. Wolf, Approximation of the invariant probability distribution of an infinite stochastic matrix, Adv. Appl. Probab. 12 (1980) 710-726. | MR | Zbl

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