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References
- Alili, L.; Doney, R. A. Wiener-Hopf factorization revisited and some applications. Stochastics Stochastics Rep. 66 (1999), no. 1-2, 87--102. MR1687803
- Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871
- Denisov, D.; Dieker, A. B.; Shneer, V. Large deviations for random walks under subexponentiality: the big-jump domain. Ann. Probab. 36 (2008), no. 5, 1946--1991. MR2440928
- Doney, R. A. A large deviation local limit theorem. Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 3, 575--577. MR0985693
- Doney, R. A. One-sided local large deviation and renewal theorems in the case of infinite mean. Probab. Theory Related Fields 107 (1997), no. 4, 451--465. MR1440141
- Doney, R. A. Local behaviour of first passage probabilities. Probab. Theory Related Fields 152 (2012), no. 3-4, 559--588. MR2892956
- Doney, R. A.; Savov, M. S. The asymptotic behavior of densities related to the supremum of a stable process. Ann. Probab. 38 (2010), no. 1, 316--326. MR2599201
- Fuk, D. H.; Nagaev, S. V. Probabilistic inequalities for sums of independent random variables. (Russian) Teor. Verojatnost. i Primenen. 16 (1971), 660--675. MR0293695
- Jones, E. M.: PhD thesis, The University of Manchester, (2008).
- Nagaev, S. V. On the asymptotic behavior of probabilities of one-sided large deviations. (Russian) Teor. Veroyatnost. i Primenen. 26 (1981), no. 2, 369--372. MR0616627
- Pruitt, William E. The growth of random walks and Lévy processes. Ann. Probab. 9 (1981), no. 6, 948--956. MR0632968
- Tchachkuk, S. G.: Limit theorems for sums of independent random variables belonging to the domain of attraction of a stable law. Candidate's dissertation, Tashent (in Russian), (1977).
- Vatutin, Vladimir A.; Wachtel, Vitali. Local probabilities for random walks conditioned to stay positive. Probab. Theory Related Fields 143 (2009), no. 1-2, 177--217. MR2449127
- Wachtel, Vitali. Local limit theorem for the maximum of asymptotically stable random walks. Probab. Theory Related Fields 152 (2012), no. 3-4, 407--424. MR2892952

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