Martin boundary of a reflected random walk on a half-space

Probability Theory and Related Fields

Volumn 148, Issue 1, 2010, Pages 197-245

  Ignatiouk Robert, Irina ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Martin boundary; Random walk; Sample path large deviations

Indexed keywords

EID: 77953698807     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-009-0228-4     Document Type: Article

References (23)

1. Billingsley P.: Convergence of Probability Measures, Wiley Series in Probability and Mathematical Statistics. Wiley, New York (1968).
2. Blinovskiǐ, V. M., Dobrushin, R. L.: Process level large deviations for a class of piecewise homogeneous random walks. The Dynkin Festschrift Progr. Probab., vol. 34, pp. 1-59. Birkhäuser, Boston (1994).
3. Borovkov A. A.: On Cramer transform, large deviations in boundary-value problems and conditional invariance principle. Sib. Math. J. 3, 493-509 (1995).
4. Borovkov A. A., Mogulskii A. A.: Large deviations for Markov chains in the positive quadrant. Russ. Math. Surv. 56(5), 803-916 (2001).
5. Dembo A., Zeitouni O.: Large Deviations Techniques and Applications. Springer, New York (1998).
6. Foley RD., McDonald DR.: Bridges and networks: exact asymptotics. Ann. Appl. Probab. 15(1B), 542-586 (2005).
7. Doob, J. L., Snell, J. L., Williamson, R. E.: Application of boundary theory to sums of independent random variables. In: Contributions to Probability and Statistics, pp. 182-197. Stanford University Press, Stanford (1960).
8. Dupuis P., Ellis R., Weiss A.: Large deviations for Markov processes with discontinuous statistics I: General upper bounds. Ann. Prob. 19(3), 1280-1297 (1991).
9. Dupuis P., Ellis R. S.: Large deviations for Markov processes with discontinuous statistics. II. Random walks. Prob. Theory Relat. Fields 91(2), 153-194 (1992).
10. Dupuis P., Ellis R. S.: The large deviation principle for a general class of queueing systems. I. Trans. Am. Math. Soc. 347(8), 2689-2751 (1995).
11. Freidlin, M. I., Wentzell, A. D.: Random Perturbations of Dynamical Systems, 2nd edn. Springer, New York (1998) Translated from the 1979 Russian original by Joseph Szücs.
12. Hennequin P. L.: Processus de Markoff en cascade. Ann. Inst. H. Poincaré 18(2), 109-196 (1963).
13. Ignatiouk-Robert I.: Sample path large deviations and convergence parameters. Ann. Appl. Prob. 11(4), 1292-1329 (2001).
14. Ignatiouk-Robert, I.: Large deviations for processes with discontinuous statistics, pp. 1479-1508 (2005).
15. Ignatiouk-Robert I.: Martin boundary of a killed random walk on a half-space. J. Theor. Probab. 21(1), 35-68 (2008).
16. Ignatyuk, I. A., Malyshev, V. A., Shcherbakov, V. V.: The influence of boundaries in problems on large deviations. Uspekhi Matematicheskikh Nauk 49, no. 2(296), 43-102 (1994).
17. Kurkova I. A., Malyshev V. A.: Martin boundary and elliptic curves. Markov Process. Relat. Fields 4, 203-272 (1998).
18. Ney P., Spitzer F.: The martin boundary for random walk. Trans. Am. Math. Soc. 121, 116-132 (1966).
19. Rockafellar, TR.: Convex analysis. Princeton University Press, Princeton (1997) Reprint of the 1970 original, Princeton Paperbacks.
20. Robert P.: Stochastic Metworks and Queues. Springer, Berlin (2003).
21. Seneta E.: Nonnegative matrices and Markov chains, 2nd edn. Springer, New York (1981).
22. Shwartz, A., Weiss, A.: Large deviations for performance analysis. Stochastic Modeling Series. Chapman & Hall, London (1995).
23. Woess W.: Random Walks on Infinite Graphs and Groups. Cambridge University Press, Cambridge (2000).