Martin boundaries associated with a killed random walk

L Alili; R. A. Doney

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 3, page 313-338
  • ISSN: 0246-0203

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Alili, L, and Doney, R. A.. "Martin boundaries associated with a killed random walk." Annales de l'I.H.P. Probabilités et statistiques 37.3 (2001): 313-338. <http://eudml.org/doc/77691>.

@article{Alili2001,
author = {Alili, L, Doney, R. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random walk; bivariate renewal process; Martin boundary},
language = {eng},
number = {3},
pages = {313-338},
publisher = {Elsevier},
title = {Martin boundaries associated with a killed random walk},
url = {http://eudml.org/doc/77691},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Alili, L
AU - Doney, R. A.
TI - Martin boundaries associated with a killed random walk
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2001
PB - Elsevier
VL - 37
IS - 3
SP - 313
EP - 338
LA - eng
KW - random walk; bivariate renewal process; Martin boundary
UR - http://eudml.org/doc/77691
ER -

References

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  1. [1] L Alili, R.A Doney, Wiener–Hopf factorisation revisited and some applications, Stochastics and Stochastics Reports66 (1999) 87-102. Zbl0928.60067MR1687803
  2. [2] J Bertoin, R.A Doney, On conditioning random walk to stay non-negative, in: Séminaire de Probabilités XXVIII, Lecture Notes in Mathematics, 1994, pp. 116-121. Zbl0814.60079MR1329107
  3. [3] R.A Doney, Last exit times for random walks, Stoch. Proc. Appl.31 (1989) 321-331. Zbl0672.60072MR998121
  4. [4] R.A Doney, One-sided local large deviation and renewal theorems in the case of infinite mean, Probab. Theory Related Fields107 (1997) 451-465. Zbl0883.60022MR1440141
  5. [5] R.A Doney, The Martin boundary for a killed random walk, J. London Math. Soc.58 (1998) 761-768. Zbl0938.60034MR1678162
  6. [6] Doney R.A., A local limit theorem for moderate deviations, Bull., London Math. Soc. (to appear). Zbl1028.60017MR1798582
  7. [7] J.L Doob, J.L Snell, R.E Williamson, Application of boundary theory to sums of independent random variables, in: Contribution to Probability and Statistics (Hotelling Anniversary Volume), 1960, pp. 182-197. Zbl0094.32202MR120667
  8. [8] W Feller, An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, NY, 1968. Zbl0155.23101MR228020
  9. [9] R.W Keener, Limit theorems for random walk conditioned to stay positive, Ann. Probab.20 (1992) 801-824. Zbl0756.60062MR1159575
  10. [10] H Kesten, Ratio theorems for random walks II, JAM (1963) 223-379. Zbl0121.35202MR163365
  11. [11] V.V Petrov, On the probabilities of large deviations for sums of independent random variables, Theor. Probab. Appl.10 (1965) 287-297. Zbl0235.60028MR185645
  12. [12] F Spitzer, Principles of Random Walk, Van Nostrand, Princeton, NJ, 1964. Zbl0119.34304MR171290

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