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Survival of homogeneous fragmentation processes with killing

Robert Knobloch, Andreas E. Kyprianou (2014)

Annales de l'I.H.P. Probabilités et statistiques

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.

Symmetric jump processes : localization, heat kernels and convergence

Richard F. Bass, Moritz Kassmann, Takashi Kumagai (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.

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