Geodesic
On the maximum of cumulative sums for the Cauchy distribution
Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 169-174

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Limit distributions for the maximum of cumulative sums of stable random variables are discussed. Some new results for the Cauchy distribution are obtained. 
@article{ZNSL_1979_85_a12,
     author = {V. B. Nevzorov},
     title = {On the maximum of cumulative sums for the {Cauchy} distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--174},
     publisher = {mathdoc},
     volume = {85},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a12/}
}
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V. B. Nevzorov. On the maximum of cumulative sums for the Cauchy distribution. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 169-174. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a12/