Survival of homogeneous fragmentation processes with killing
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, p. 476-491

We consider a homogeneous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the decay of the largest fragment for parameter values that allow for survival. In this respect the present paper is also concerned with the probability of extinction of the killed process.

Nous considérons un processus de fragmentation homogène tué à une barrière exponentielle. À l'aide de deux familles de martingales nous analysons la décroissance du plus gros fragment pour des valeurs des paramètres permettant la survie du système. Cet article traite aussi de la probabilité d'extinction du processus tué.

DOI : https://doi.org/10.1214/12-AIHP520
Classification:  60J25,  60G09
Keywords: homogeneous fragmentation, scale functions, additive martingales, multiplicative martingales, largest fragment
@article{AIHPB_2014__50_2_476_0,
     author = {Knobloch, Robert and Kyprianou, Andreas E.},
     title = {Survival of homogeneous fragmentation processes with killing},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {2014},
     pages = {476-491},
     doi = {10.1214/12-AIHP520},
     zbl = {1301.60087},
     mrnumber = {3189080},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_2_476_0}
}
Knobloch, Robert; Kyprianou, Andreas E. Survival of homogeneous fragmentation processes with killing. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 476-491. doi : 10.1214/12-AIHP520. http://www.numdam.org/item/AIHPB_2014__50_2_476_0/

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