Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables
Annales de l'I.H.P. Probabilités et statistiques, Volume 30 (1994) no. 3, p. 467-499 
@article{AIHPB_1994__30_3_467_0,
     author = {Marcus, Michael B. and Rosen, Jay},
     title = {Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of L\'evy processes and Random walks in the domain of attraction of Cauchy random variables},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {30},
     number = {3},
     year = {1994},
     pages = {467-499},
     zbl = {0805.60069},
     mrnumber = {1288360},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1994__30_3_467_0}
}

Marcus, Michael B.; Rosen, Jay. Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables. Annales de l'I.H.P. Probabilités et statistiques, Volume 30 (1994) no. 3, pp. 467-499. http://www.numdam.org/item/AIHPB_1994__30_3_467_0/

[BGT] N. Bingham, C. Goldie and J. Teugels, Regular Variation, 1987, Cambridge Univ. | MR 898871 | Zbl 0617.26001

[ET] P. Erdös and S.J. Taylor, Some problems concerning the structure of random walk paths, Acta Math. Acad. Sci. Hung., 11, 1960, p. 137-162. | MR 121870 | Zbl 0091.13303

[F] B. Fristedt, Sample functions of stochastic processes with stationary independent increments, Advances in Probability and Related Topics, 3, 1974, p. 241-396, Marcel Dekker, NY. | MR 400406 | Zbl 0309.60047

[FP] B. Fristedt and W. Pruitt, Lower functions for increasing random walks and subordinators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 18, 1971, p. 167-182. | MR 292163 | Zbl 0197.44204

[K] H. Kesten, Hitting probabilities of single points for processes with stationary independent increments, Memoir N° 93, 1969, Amer. Math. Soc. | MR 272059 | Zbl 0186.50202

[Ka] J.P. Kahane, Some random series of functions, Heath Math. Monographs, 1968, Cambridge Univ. Press, 1985, 2nd edn. | MR 833073 | Zbl 0192.53801

[MR1] M.B. Marcus and J. Rosen, Laws of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks, 1992, Annals of Probability, To appear. | MR 1288125 | Zbl 0815.60073

[MR2] M.B. Marcus and J. Rosen, Moment generating functions for the local times of symmetric Markov processes and random walks, Probability in Banach Spaces, 8, 30, 1992, p. 364-378, Birkhauser, Boston. | MR 1227631 | Zbl 0788.60092

[P] E.J.G. Pitman, Some theorems on characteristic functions of probability distributions, Proc. Fourth Berkeley Symposium, II, 1961, p. 393-402, Univ. of California Press, Berkeley. | MR 132568 | Zbl 0101.35201