Geodesic
Asymptotic behavior of the conditional probability of the nonlinear boundary crossing by a random walk
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 12-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the asymptotic behavior of the conditional probability of the boundary crossing by a random walk with distribution belonging to the attraction domain of a stable distribution with parameter $\alpha$.
Keywords: Random walk, nonlinear boundary crossing, limit theorems
Mots-clés : stable distribution. 
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S. A. Aliev; T. E. Hashimova. Asymptotic behavior of the conditional probability of the nonlinear boundary crossing by a random walk. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 12-16. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a1/

[1] A. A. Borovkov, A. A. Mogulskii, “Limit theorems in the problem of the boundary crossing by a multivariate walk”, Sib. Mat. Zh., 42:2 (2001), 284–318

[2] M. Woodroofe, Nonlinear Renewal Theory in Sequential Analysis, SIAM, Philadelphia, 1982

[3] D. Siegmund, Sequential Analysis. Tests and Confidence Intervals, Springer, New York, 1985

[4] F. H. Ragimov, “On the limit behavior of conditional probabilities of the crossing of nonlinear boundaries by a perturbed random walk”, Transactions of the NAS of Azerbaijan, 2006, no. 1, 163–168

[5] F. H. Ragimov, “Asymptotic expansion of the distribution of the crossing time for nonlinear boundaries”, Teor. Veroyat. Primen., 37 (1992), 580–583

[6] I. A. Ibrahimov, Yu. V. Linnik, Independent and Stationary Sequences of Random Variables, Wolter-Noordhoff, Groningen, 1971

[7] W. Feller, An Introduction to Probability Theory and Its Applications, Wiley, New York, 1970