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

Journal of Theoretical Probability

Volumn 21, Issue 1, 2008, Pages 35-68

  Ignatiouk Robert, Irina ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Martin boundary; Random walk; Sample path large deviations

Indexed keywords

EID: 38349088355     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-007-0100-3     Document Type: Article

References (24)

1. Alili, L., Doney, R.A.: Martin boundaries associated with a killed random walk. Ann. Inst. H. Poincaré Probab. Stat. 37(3), 313-338 (2001)
2. Billingsley, P.: Convergence of Probability Measures. Wiley Series in Probability and Mathematical Statistics. Wiley, New York (1968)
3. Borovkov, A.A., Mogulskii, A.A.: The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks. Sib. Math. J. 33(4), 745-782 (1992)
4. Cartier, P.: Fonctions harmoniques sur un arbre. Symposia Math. 9, 203-270 (1972)
5. Davis, B., McDonald, D.: An elementary proof of the local central limit theorem. J. Theor. Probab. 8, 693-701 (1995)
6. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Springer, New York (1998)
7. Foley, R.D., McDonald, D.R.: Bridges and networks: exact asymptotics. Ann. Appl. Probab. 15(1B), 542-586 (2005)
8. Doney, R.A.: The Martin boundary and ratio limit theorems for killed random walks. J. Lond. Math. Soc. 2(58), 761-768 (1998)
9. Doob, J.L.: Discrete potential theory and boundaries. J. Math. Mech. 8, 433-458 (1959)
10. Dynkin, E.B.: Boundary theory of Markov processes. Russ. Math. Surv. 24(7), 1-42 (1969)
11. Hennequin, P.L.: Processus de Markoff en cascade. Ann. Inst. H. Poincaré 18(2), 109-196 (1963)
12. Hunt, G.A.: Markoff chains and Martin boundaries. Illinois J. Math. 4, 313-340 (1960)
13. Ignatiouk-Robert, I.: Sample path large deviations and convergence parameters. Ann. Appl. Probab. 11(4), 1292-1329 (2001)
14. Ignatiouk-Robert, I.: Martin boundary of a reflected random walk on a half-space. Preprint: http://arxiv.org/abs/math.PR/0610242 (2006)
15. Kurkova, I.A., Malyshev, V.A.: Martin boundary and elliptic curves. Markov Process. Relat. Fields 4, 203-272 (1998)
16. Martin, R.S.: Minimal positive harmonic functions. Trans. Am. Math. Soc. 49, 137-172 (1941)
17. McDonald, D.: On local limit theorems for integer valued random variables. Theory Probab. Appl. 24, 613-619 (1979)
18. Ney, P., Spitzer, F.: The Martin boundary for random walk. Trans. Am. Math. Soc. 121, 116-132 (1966)
19. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1997). Reprint of the 1970 original, Princeton Paperbacks
20. Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes, and Martingales. Vol. 1: Foundations, 2nd edn. Wiley, Chichester (1994)
21. Rudin, W.: Real and Complex Analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill, Ney York (1974)
22. Seneta, E.: Nonnegative Matrices and Markov Chains, 2nd edn. Springer, New York (1981)
23. Spitzer, F.: Principles of Random Walk. D. van Nostrand Company, INC (1964)
24. Woess, W.: Random Walks on Infinite Graphs and Groups. Cambridge University Press, Cambridge (2000)