Geodesic
General scheme of maxima of sums of independent random variables and its applications
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 544-550

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A general scheme of maxima of sums of independent random variables is introduced. We prove a theorem on the convergence of the maxima in probability. We study its applications to large jumps in random walks and to extrema of shot-noise fields in the case of regularly varying tails. Nondegenerate limiting laws are obtained. 
@article{MZM_2005_77_4_a7,
     author = {A. V. Lebedev},
     title = {General scheme of maxima of sums of independent random variables and its applications},
     journal = {Matemati\v{c}eskie zametki},
     pages = {544--550},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a7/}
}
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A. V. Lebedev. General scheme of maxima of sums of independent random variables and its applications. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 544-550. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a7/