Geodesic
Renewal shot noise processes in the case of slowly varying tails
Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 14-21

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We investigate weak convergence of renewal shot noise processes in the case of slowly varying tails of the inter-shot times. We show that these processes, after an appropriate non-linear scaling, converge in the sense of finite-dimensional distributions to an inverse extremal process.
Keywords: Extremal process, random process with immigration, renewal theory, shot noise process. 
@article{THSP_2016_21_2_a2,
     author = {Zakhar Kabluchko and Alexander Marynych},
     title = {Renewal shot noise processes in the case of slowly varying tails},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {14--21},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a2/}
}
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Zakhar Kabluchko; Alexander Marynych. Renewal shot noise processes in the case of slowly varying tails. Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 14-21. http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a2/