K. K. Anderson and K. B. Athreya, A note on conjugate ??-variation and a weak limit theorem for the number of renewals, Statistics & Probability Letters, vol.6, issue.3, pp.151-154, 1988.
DOI : 10.1016/0167-7152(88)90111-3

Q. Berger, Local large deviation and renewal theorems for multivariate renewals, work in progress

N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variations, 1987.
DOI : 10.1017/CBO9780511721434

A. A. Borovkov, On the asymptotics of distributions of first-passage times. I., Math. Notes, pp.24-39, 2004.

A. A. Borovkov, On the Asymptotic Behavior of Distributions of First-Passage Times, II, Mathematical Notes, vol.75, issue.3/4, pp.322-330, 2004.
DOI : 10.1023/B:MATN.0000023311.52852.25

T. Budd, N. Curien, and C. Marzouk, Infinite random planar maps related to Cauchy processes, preprint

F. Caravenna and R. Doney, Local Large Deviations and the Strong Renewal Theorem, preprint

J. Chover, P. Ney, and S. Wainger, Functions of probability measures, Journal d'Analyse Math??matique, vol.26, issue.1, pp.255-302, 1973.
DOI : 10.1007/978-3-642-51866-9

D. B. Cline and T. Hsing, Large deviation probabilities for sums of random variables with heavy or subexponential tails, 1994.

D. Denisov, A. B. Dieker, and V. Shneer, Large deviations for random walks under subexponentiality: The big-jump domain, The Annals of Probability, vol.36, issue.5, pp.1946-199, 2008.
DOI : 10.1214/07-AOP382

R. A. Doney, On the exact asymptotic behavior of the distribution of ladder epochs, Stoch, Proc. Appl. 12 pp, pp.203-214, 1982.

R. A. Doney, On the asymptotic behaviour of first passage times for transient random walks, Probab. Theory Relat. Fields, pp.239-246, 1989.

R. A. Doney, One-sided local large deviation and renewal theorems in the case of infinite mean, Probability Theory and Related Fields, vol.107, issue.4, pp.451-465, 1997.
DOI : 10.1007/s004400050093

K. B. Erickson, Strong renewal theorems with infinite mean, Transaction of the Americ, Math. Soc, vol.151, 1970.

W. Feller, An introduction to probability theory and its applications, 1971.

P. Flajolet and A. , Singularity Analysis of Generating Functions, SIAM Journal on Discrete Mathematics, vol.3, issue.2, pp.216-240, 1990.
DOI : 10.1137/0403019
URL : https://hal.archives-ouvertes.fr/inria-00075725

A. Garsia and J. Lamperti, A discrete renewal theorem with infinite mean, Commentarii Mathematici Helvetici, vol.37, issue.1, pp.221-234, 1963.
DOI : 10.1007/BF02566974

B. V. Gnedenko and A. N. Kolmogorov, Limit Theorems for Sums of Independent Random Variables, 1954.

L. De-haan and S. I. Resnick, Conjugate $\Pi$-Variation and Process Inversion, The Annals of Probability, vol.7, issue.6, pp.1028-1035, 1979.
DOI : 10.1214/aop/1176994895

A. V. Nagaev, Large deviations of sums of independent random variables, The Annals of Probability, pp.745-789, 1979.

B. A. Rogozin, The Distribution of the First Ladder Moment and Height and Fluctuation of a Random Walk, Theory of Probability & Its Applications, vol.16, issue.4, pp.575-595323, 1956.
DOI : 10.1137/1116067

V. A. Vatutin and V. Wachtel, Local probabilities for random walks conditioned to stay positive, Probab. Theory Relat, pp.177-217, 2009.
DOI : 10.1007/s00440-007-0124-8
URL : http://arxiv.org/pdf/0711.1302

R. Wei, On the Long-Range Directed Polymer Model, Journal of Statistical Physics, vol.138, issue.3???4, pp.320-350, 2016.
DOI : 10.1007/s00440-006-0030-5

J. A. Williamson, Random walks and Riesz kernels, Pacific Journal of Mathematics, vol.25, issue.2, 1968.
DOI : 10.2140/pjm.1968.25.393
URL : http://msp.org/pjm/1968/25-2/pjm-v25-n2-p15-s.pdf

V. M. Zolotarev, One-dimensional stable distributions, Amer. Math. Soc., Providence RI, vol.65, issue.5, 1986.
DOI : 10.1090/mmono/065