no. 1
Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) no. 1, pp. 49-83. 
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     title = {Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {49--83},
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     mrnumber = {1669920},
     zbl = {0922.60044},
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     url = {http://www.numdam.org/item/AIHPB_1999__35_1_49_0/}
}
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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) no. 1, pp. 49-83. http://www.numdam.org/item/AIHPB_1999__35_1_49_0/

[1] S. Aspandiiarov, On the convergence of 2-dimensional Markov chains in quadrants with boundary reflection, Stoch. and Stochastic Reports., Vol. 53, 1995, pp. 275-303. | MR | Zbl

[2] S. Aspandiiarov, R. Iasnogorodski and M. Menshikov, 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 | Zbl

[3] S. Aspandiiarov, R. Iasnogorodski and M. Menshikov, Reflected random walks in a three-dimensional orthant (in preparation).

[4] S. Aspandiiarov and R. Iasnogorodski, 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 | Zbl

[5] S. Aspandiiarov and Iasnogorodski, 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

[6] S. Aspandiiarov and Iasnogorodski, Asymptotic behavior of stationary distributions for countable Markov chains with some applications. Bernoulli (to appear). | MR | Zbl

[7] Kai Lai Chung, Markov Chains with Stationary Transition Probabilities. Springer, Berlin, 1967. | MR | Zbl

[8] J. Dai and R.J. Williams, Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theory of Prob. and its Appl., Vol. 40, 1996, pp. 1-25. | Zbl

[9] R.D. De Blassie, Explicit semimartingale representation of Brownian motion in a wedge. Stoch. Proc. Appl., Vol. 34, 1990 pp. 67-97. | MR | Zbl

[10] S.N. Ethier, T.G. Kurtz, Markov Processes. Wiley, Chichester, 1986. | MR | Zbl

[11] J.M. Harrison, R.J. Williams, Brownian models of open queuing networks with homogeneous customer populations. Stochastics and Stoch. Reports., Vol. 22, 1987, pp. 77-115. | MR | Zbl

[12] G. Fayolle, V. Malyshev and M. Menshikov, Random walks in a quarter plane with zero drifts. Ann. Inst. H. Poincare., Vol. 28, 1992, pp. 179-195. | Numdam | MR | Zbl

[13] W. Feller, An Introduction to Probability Theory and its Applications. Wiley, 2nd edn, New York, 1971. | MR | Zbl

[14] J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes. Springer, Berlin, 1987. | MR | Zbl

[15] N.C. Jain, K. Jogdeo and W.F. Stout, Upper and lower functions for martingales and mixing processes. Ann. Prob., Vol. 3, 1975, pp. 119-145. | MR | Zbl

[16] R.Sh. Liptzer, A.N. Shiryaev, Theory of Martingales. Kluwer, Dordrecht, 1989.

[17] M. Menshikov and R.J. Williams, Passage-time moments for continuous non-negative stochastic processes and applications. Adv. Appl. Prob. (to appear). | Zbl

[18] J. Neveu, Discrete-Parameter Martingales. North-Holland, Amsterdam, 1975. | MR | Zbl

[19] W.P. Petersen, Diffusion approximations for networks of queues with multiple customer types. Math. Oper. Res., Vol. 9, 1991, pp. 90-118.

[20] V. Petrov, Sums of Independent Random Variables. Springer-Verlag, 1975. | MR | Zbl

[21] W. Pruitt, The growth of random walks and Lévy processes. Ann. Prob., Vol. 9, 1981, pp. 948-956. | MR | Zbl

[22] M.I. Reiman, Open queuing networks in heavy traffic. Math. Oper. Res., Vol. 9, 1984, pp. 441-458. | MR | Zbl

[23] D. Revuz, Markov Chains. North-Holland, Amsterdam, 1975. | MR | Zbl

[24] L.M. Taylor and R.J. Williams, Existence and uniqueness of SRBM in an orthant. Prob. Theory and Rel. Fields., Vol. 96, 1993, pp. 283-318. | Zbl

[25] S.R.S. Varadhan, R.J. Williams, Brownian motion in a wedge with oblique reflection. Comm. Pure and Applied Math., Vol. 38, 1985, pp. 405-443. | MR | Zbl

[26] R.J. Williams, 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

[27] R.J. Williams, Semimartingale reflecting Brownian motion in the orthant. The IMA Volumes in Mathematics and its Applications., Vol. 71, Springer, Berlin, 1995. | MR | Zbl

[28] R.J. Williams, Reflected Brownian motion in a wedge: semimartingale property. Z. Wahr. verw. Geb., Vol. 69, 1985 pp; 161-176. | MR | Zbl