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, Volume 35 (1999) no. 6, p. 685-734
@article{AIHPB_1999__35_6_685_0,
     author = {Kesten, Harry and Maller, R. A.},
     title = {Stability and other limit laws for exit times of random walks from a strip or a halfplane},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {35},
     number = {6},
     year = {1999},
     pages = {685-734},
     zbl = {0940.60064},
     mrnumber = {1725708},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1999__35_6_685_0}
}
Kesten, Harry; 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, Volume 35 (1999) no. 6, pp. 685-734. http://www.numdam.org/item/AIHPB_1999__35_6_685_0/

[1] J. Bertoin and R.A. Doney, Spitzer's condition for random walks and Lévy processes, Ann. Inst. Henri Poincaré 33 (1997) 167-178. | Numdam | MR 1443955 | Zbl 0880.60078

[2] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation, Cambridge Univ. Press, 1987. | MR 898871 | Zbl 0617.26001

[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. | MR 125609 | Zbl 0099.35103

[4] Y.S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, 2nd edn., Springer, 1988. | MR 953964 | Zbl 0652.60001

[5] C.G. Esseen, On the concentration function of a sum of independent random variables, Z. Wahrsch. verw. Geb. 9 (1968) 290-308. | MR 231419 | Zbl 0195.19303

[6] W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, 1971. | MR 270403 | Zbl 0219.60003

[7] B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, 2nd edn., Addison-Wesley, Reading, MA, 1968. | MR 233400 | Zbl 0056.36001

[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. | MR 1618833 | Zbl 0905.60064

[9] A. Gut, O. Klesov and J. Steinebach, Equivalence in strong limit theorems for renewal counting processes, Statist. Probab. Lett. 35 (1997) 381-394. | MR 1483025 | Zbl 0885.60026

[10] C.C. Heyde, Some renewal theorems with application to a first passage problem, Ann. Math. Statist. 37 (1966) 699-710. | MR 193692 | Zbl 0143.19102

[11] H. Kesten, Problem 5716, Amer. Math. Monthly 77 (1970) 197 and 78 (1971) 385-388. | MR 1536265

[12] H. Kesten and R.A. Maller, Ratios of trimmed sums and order statistics, Ann. Probab. 20 (1992) 1805-1842. | MR 1188043 | Zbl 0764.60034

[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. | MR 1303651 | Zbl 0816.60067

[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. | MR 1337473 | Zbl 0835.60022

[15] H. Kesten and R.A. Maller, Two renewal theorems for general random walks tending to infinity, Probab. Theory Related Fields 106 (1996 ) 1-38. | MR 1408415 | Zbl 0855.60080

[16] H. Kesten and R.A. Maller, Divergence of a random walk through deterministic and random subsequences, J. Theor. Probab. 10 (1997) 395-427. | MR 1455151 | Zbl 0884.60067

[17] S.B. Kochen and C.J. Stone, A note on the Borel-Cantelli lemma, Ill. J. Math. 8 (1964) 248-251. | MR 161355 | Zbl 0139.35401

[18] R.A. Maller, Relative stability and the strong law of large numbers, Z. Wahrsch. verw. Geb. 43 (1978) 141-148. | MR 501295 | Zbl 0366.60035

[19] W.E. Pruitt, The growth of random walks and Lévy processes, Ann. Probab. 9 (1981) 948-956. | MR 632968 | Zbl 0477.60033

[20] B.A. Rogozin, Relatively stable walks, Theory Probab. Appl. 21 (1976) 375-379. | MR 423542 | Zbl 0381.60043

[21] F. Spitzer, Principles of Random Walk, 2nd edn., Springer, New York, 1976. | Zbl 0359.60003

[22] M. Woodroofe, Nonlinear Renewal Theory in Sequential Analysis, Regional Conf. Series in Appl. Math. Soc. for Indust. and Appl. Math., 1982. | MR 660065 | Zbl 0487.62062