Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Survival of homogeneous fragmentation processes with killing

Robert Knobloch and Andreas E. Kyprianou

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 2 (2014), 476-491.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1395856136

Digital Object Identifier
doi:10.1214/12-AIHP520

Mathematical Reviews number (MathSciNet)
MR3189080

Zentralblatt MATH identifier
1301.60087

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60G09: Exchangeability

Keywords
Homogeneous fragmentation Scale functions Additive martingales Multiplicative martingales Largest fragment

Citation

Knobloch, Robert; Kyprianou, Andreas E. Survival of homogeneous fragmentation processes with killing. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 2, 476--491. doi:10.1214/12-AIHP520. https://projecteuclid.org/euclid.aihp/1395856136


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