@article{AIHPB_1999__35_1_49_0, author = {Aspandiiarov, Sanjar and Iasnogorodski, Roudolf}, title = {Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, volume = {35}, year = {1999}, pages = {49-83}, mrnumber = {1669920}, zbl = {0922.60044}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPB_1999__35_1_49_0} }
Aspandiiarov, Sanjar; Iasnogorodski, Roudolf. Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) pp. 49-83. http://gdmltest.u-ga.fr/item/AIHPB_1999__35_1_49_0/
[1] On the convergence of 2-dimensional Markov chains in quadrants with boundary reflection, Stoch. and Stochastic Reports., Vol. 53, 1995, pp. 275-303. | MR 1381681 | Zbl 0854.60030
,[2] Passage-time moments for non-negative stochastic processes and an application to reflected random walks in a quadrant. Ann. Prob., Vol. 26, 1996, pp. 932-960. | MR 1404537 | Zbl 0869.60036
, and ,[3] Reflected random walks in a three-dimensional orthant (in preparation).
, and ,[4] Tails of passage-times for non-negative stochastic processes and an application to stochastic processes with boundary reflection in a wedge. Stoch. Proc. Appl., Vol. 66, 1997 pp. 115-145. | MR 1431874 | Zbl 0889.60045
and ,[5] General criteria of integrability of functions of passage-times for non-negative stochastic processes and their applications. Theory of Prob. and its Appl. (to appear). | Zbl 0953.60062
and ,[6] Asymptotic behavior of stationary distributions for countable Markov chains with some applications. Bernoulli (to appear). | MR 1693596 | Zbl 0948.60068
and ,[7] Markov Chains with Stationary Transition Probabilities. Springer, Berlin, 1967. | MR 116388 | Zbl 0146.38401
,[8] Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theory of Prob. and its Appl., Vol. 40, 1996, pp. 1-25. | Zbl 0854.60078
and ,[9] Explicit semimartingale representation of Brownian motion in a wedge. Stoch. Proc. Appl., Vol. 34, 1990 pp. 67-97. | MR 1039563 | Zbl 0694.60076
,[10] Markov Processes. Wiley, Chichester, 1986. | MR 838085 | Zbl 0592.60049
, ,[11] Brownian models of open queuing networks with homogeneous customer populations. Stochastics and Stoch. Reports., Vol. 22, 1987, pp. 77-115. | MR 912049 | Zbl 0632.60095
, ,[12] Random walks in a quarter plane with zero drifts. Ann. Inst. H. Poincare., Vol. 28, 1992, pp. 179-195. | Numdam | MR 1162572 | Zbl 0747.60064
, and ,[13] An Introduction to Probability Theory and its Applications. Wiley, 2nd edn, New York, 1971. | MR 270403 | Zbl 0219.60003
,[14] Limit Theorems for Stochastic Processes. Springer, Berlin, 1987. | MR 959133 | Zbl 0635.60021
and ,[15] Upper and lower functions for martingales and mixing processes. Ann. Prob., Vol. 3, 1975, pp. 119-145. | MR 368130 | Zbl 0301.60026
, and ,[16]
, , Theory of Martingales. Kluwer, Dordrecht, 1989.[17] Passage-time moments for continuous non-negative stochastic processes and applications. Adv. Appl. Prob. (to appear). | Zbl 0857.60042
and ,[18] Discrete-Parameter Martingales. North-Holland, Amsterdam, 1975. | MR 402915 | Zbl 0345.60026
,[19] Diffusion approximations for networks of queues with multiple customer types. Math. Oper. Res., Vol. 9, 1991, pp. 90-118.
,[20] Sums of Independent Random Variables. Springer-Verlag, 1975. | MR 388499 | Zbl 0322.60042
,[21] The growth of random walks and Lévy processes. Ann. Prob., Vol. 9, 1981, pp. 948-956. | MR 632968 | Zbl 0477.60033
,[22] Open queuing networks in heavy traffic. Math. Oper. Res., Vol. 9, 1984, pp. 441-458. | MR 757317 | Zbl 0549.90043
,[23] Markov Chains. North-Holland, Amsterdam, 1975. | MR 415773 | Zbl 0332.60045
,[24] Existence and uniqueness of SRBM in an orthant. Prob. Theory and Rel. Fields., Vol. 96, 1993, pp. 283-318. | Zbl 0794.60079
and ,[25] Brownian motion in a wedge with oblique reflection. Comm. Pure and Applied Math., Vol. 38, 1985, pp. 405-443. | MR 792398 | Zbl 0579.60082
, ,[26] On the approximation of queuing networks in heavy traffic. Stochastic Networks: Theory and Applications, eds. F. P. Kelly, S. Zachary and I. Ziedins, Clarendon Press, Oxford, 1996, pp. 35-56. | Zbl 0855.60083
,[27] Semimartingale reflecting Brownian motion in the orthant. The IMA Volumes in Mathematics and its Applications., Vol. 71, Springer, Berlin, 1995. | MR 1381009 | Zbl 0827.60031
,[28] Reflected Brownian motion in a wedge: semimartingale property. Z. Wahr. verw. Geb., Vol. 69, 1985 pp; 161-176. | MR 779455 | Zbl 0535.60042
,