A note on the two-sided regulated random walk

Manita, A.; Simonot, F.

doi:10.1016/j.anihpb.2003.06.002

Manita, A. ; Simonot, F.

Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 1, pp. 43-52

MR Zbl

DOI : 10.1016/j.anihpb.2003.06.002

@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},
     pages = {43--52},
     year = {2004},
     publisher = {Elsevier},
     volume = {40},
     number = {1},
     doi = {10.1016/j.anihpb.2003.06.002},
     mrnumber = {2037472},
     zbl = {1037.60083},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2003.06.002/}
}

TY  - JOUR
AU  - Manita, A.
AU  - Simonot, F.
TI  - A note on the two-sided regulated random walk
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2004
SP  - 43
EP  - 52
VL  - 40
IS  - 1
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2003.06.002/
DO  - 10.1016/j.anihpb.2003.06.002
LA  - en
ID  - AIHPB_2004__40_1_43_0
ER  -

%0 Journal Article
%A Manita, A.
%A Simonot, F.
%T A note on the two-sided regulated random walk
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2004
%P 43-52
%V 40
%N 1
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2003.06.002/
%R 10.1016/j.anihpb.2003.06.002
%G en
%F 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) no. 1, pp. 43-52. doi: 10.1016/j.anihpb.2003.06.002

Bibliographie
Cité par

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

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

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

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

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

Cité par Sources :