Stability and other limit laws for exit times of random walks from a strip or a halfplane

Harry Kesten; R. A. Maller

Annales de l'I.H.P. Probabilités et statistiques (1999)

  • Volume: 35, Issue: 6, page 685-734
  • ISSN: 0246-0203

How to cite

top

Kesten, Harry, and Maller, R. A.. "Stability and other limit laws for exit times of random walks from a strip or a halfplane." Annales de l'I.H.P. Probabilités et statistiques 35.6 (1999): 685-734. <http://eudml.org/doc/77643>.

@article{Kesten1999,
author = {Kesten, Harry, Maller, R. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {relatively stable random walk; passage time; sequential analysis; stability of the maximal sum},
language = {eng},
number = {6},
pages = {685-734},
publisher = {Gauthier-Villars},
title = {Stability and other limit laws for exit times of random walks from a strip or a halfplane},
url = {http://eudml.org/doc/77643},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Kesten, Harry
AU - Maller, R. A.
TI - Stability and other limit laws for exit times of random walks from a strip or a halfplane
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1999
PB - Gauthier-Villars
VL - 35
IS - 6
SP - 685
EP - 734
LA - eng
KW - relatively stable random walk; passage time; sequential analysis; stability of the maximal sum
UR - http://eudml.org/doc/77643
ER -

References

top
  1. [1] J. Bertoin and R.A. Doney, Spitzer's condition for random walks and Lévy processes, Ann. Inst. Henri Poincaré33 (1997) 167-178. Zbl0880.60078MR1443955
  2. [2] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation, Cambridge Univ. Press, 1987. Zbl0617.26001MR898871
  3. [3] Y.S. Chow and H. Robbins, On sums of independent random variables with infinite moments and 'fair' games, Proc. Nat. Acad. Sci.47 (1961) 330-335. Zbl0099.35103MR125609
  4. [4] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 2nd edn., Springer, 1988. Zbl0652.60001MR953964
  5. [5] C.G. Esseen, On the concentration function of a sum of independent random variables, Z. Wahrsch. verw. Geb.9 (1968) 290-308. Zbl0195.19303MR231419
  6. [6] W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, 1971. Zbl0219.60003MR270403
  7. [7] B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, 2nd edn., Addison-Wesley, Reading, MA, 1968. Zbl0056.36001MR233400
  8. [8] P.S. Griffin and R.A. Maller, On the rate of growth of the overshoot and the maximum partial sum, Adv. Appl. Prob.30 (1998) 181-196. Zbl0905.60064MR1618833
  9. [9] A. Gut, O. Klesov and J. Steinebach, Equivalence in strong limit theorems for renewal counting processes, Statist. Probab. Lett.35 (1997) 381-394. Zbl0885.60026MR1483025
  10. [10] C.C. Heyde, Some renewal theorems with application to a first passage problem, Ann. Math. Statist.37 (1966) 699-710. Zbl0143.19102MR193692
  11. [11] H. Kesten, Problem 5716, Amer. Math. Monthly77 (1970) 197 and 78 (1971) 385-388. MR1536265
  12. [12] H. Kesten and R.A. Maller, Ratios of trimmed sums and order statistics, Ann. Probab.20 (1992) 1805-1842. Zbl0764.60034MR1188043
  13. [13] H. Kesten and R.A. Maller, Infinite limits and infinite limit points of random walks and trimmed sums, Ann. Probab.22 (1994) 1473-1513. Zbl0816.60067MR1303651
  14. [14] H. Kesten and R.A. Maller, The effect of trimming on the law of large numbers, Proc. Lond. Math. Soc.71 (1995) 441-480. Zbl0835.60022MR1337473
  15. [15] H. Kesten and R.A. Maller, Two renewal theorems for general random walks tending to infinity, Probab. Theory Related Fields106 (1996 ) 1-38. Zbl0855.60080MR1408415
  16. [16] H. Kesten and R.A. Maller, Divergence of a random walk through deterministic and random subsequences, J. Theor. Probab.10 (1997) 395-427. Zbl0884.60067MR1455151
  17. [17] S.B. Kochen and C.J. Stone, A note on the Borel-Cantelli lemma, Ill. J. Math.8 (1964) 248-251. Zbl0139.35401MR161355
  18. [18] R.A. Maller, Relative stability and the strong law of large numbers, Z. Wahrsch. verw. Geb.43 (1978) 141-148. Zbl0366.60035MR501295
  19. [19] W.E. Pruitt, The growth of random walks and Lévy processes, Ann. Probab.9 (1981) 948-956. Zbl0477.60033MR632968
  20. [20] B.A. Rogozin, Relatively stable walks, Theory Probab. Appl.21 (1976) 375-379. Zbl0381.60043MR423542
  21. [21] F. Spitzer, Principles of Random Walk, 2nd edn., Springer, New York, 1976. Zbl0359.60003
  22. [22] M. Woodroofe, Nonlinear Renewal Theory in Sequential Analysis, Regional Conf. Series in Appl. Math. Soc. for Indust. and Appl. Math., 1982. Zbl0487.62062MR660065

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.