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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.