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 (1999)
- Volume: 35, Issue: 6, page 685-734
- ISSN: 0246-0203
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topKesten, 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] 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] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation, Cambridge Univ. Press, 1987. Zbl0617.26001MR898871
- [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] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 2nd edn., Springer, 1988. Zbl0652.60001MR953964
- [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] W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, 1971. Zbl0219.60003MR270403
- [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] 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] 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] C.C. Heyde, Some renewal theorems with application to a first passage problem, Ann. Math. Statist.37 (1966) 699-710. Zbl0143.19102MR193692
- [11] H. Kesten, Problem 5716, Amer. Math. Monthly77 (1970) 197 and 78 (1971) 385-388. MR1536265
- [12] H. Kesten and R.A. Maller, Ratios of trimmed sums and order statistics, Ann. Probab.20 (1992) 1805-1842. Zbl0764.60034MR1188043
- [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] 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] 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] 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] S.B. Kochen and C.J. Stone, A note on the Borel-Cantelli lemma, Ill. J. Math.8 (1964) 248-251. Zbl0139.35401MR161355
- [18] R.A. Maller, Relative stability and the strong law of large numbers, Z. Wahrsch. verw. Geb.43 (1978) 141-148. Zbl0366.60035MR501295
- [19] W.E. Pruitt, The growth of random walks and Lévy processes, Ann. Probab.9 (1981) 948-956. Zbl0477.60033MR632968
- [20] B.A. Rogozin, Relatively stable walks, Theory Probab. Appl.21 (1976) 375-379. Zbl0381.60043MR423542
- [21] F. Spitzer, Principles of Random Walk, 2nd edn., Springer, New York, 1976. Zbl0359.60003
- [22] M. Woodroofe, Nonlinear Renewal Theory in Sequential Analysis, Regional Conf. Series in Appl. Math. Soc. for Indust. and Appl. Math., 1982. Zbl0487.62062MR660065
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