Martin boundaries associated with a killed random walk

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 37, Issue 3, 2001, Pages 313-338

  Alili, L ^a   Doney, R A ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

60J15; 60K05

Indexed keywords

EID: 0042334599     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(00)01069-4     Document Type: Article

References (12)

1. Alili L., Doney R.A. Wiener-Hopf factorisation revisited and some applications. Stochastics and Stochastics Reports. 66:1999;87-102.
2. Bertoin J., Doney R.A. On conditioning random walk to stay non-negative. Séminaire de Probabilités XXVIII. Lecture Notes in Mathematics. 1994;116-121.
3. Doney R.A. Last exit times for random walks. Stoch. Proc. Appl. 31:1989;321-331.
4. Doney R.A. One-sided local large deviation and renewal theorems in the case of infinite mean. Probab. Theory Related Fields. 107:1997;451-465.
5. Doney R.A. The Martin boundary for a killed random walk. J. London Math. Soc. 58:1998;761-768.
6. Doney R.A., A local limit theorem for moderate deviations, Bull., London Math. Soc. (to appear).
7. Doob J.L., Snell J.L., Williamson R.E. Application of boundary theory to sums of independent random variables. Contribution to Probability and Statistics (Hotelling Anniversary Volume). 1960;182-197.
8. Feller W. An Introduction to Probability Theory and its Applications, Vol. 2. 2nd edn. 1968;Wiley, NY.
9. Keener R.W. Limit theorems for random walk conditioned to stay positive. Ann. Probab. 20:1992;801-824.
10. Kesten H. Ratio theorems for random walks II. JAM. 1963;223-379.
11. Petrov V.V. On the probabilities of large deviations for sums of independent random variables. Theor. Probab. Appl. 10:1965;287-297.
12. Spitzer F. Principles of Random Walk. 1964;Van Nostrand, Princeton, NJ.