Survival of homogeneous fragmentation processes with killing
Robert Knobloch, Andreas E. Kyprianou
TL;DR
This paper analyzes the survival and extinction probabilities of a homogeneous fragmentation process with killing at an exponential barrier, using martingales to study the growth of the largest fragment.
Contribution
It introduces a martingale-based framework to analyze the growth and extinction probabilities in a killed fragmentation process.
Findings
Characterization of the growth of the largest fragment.
Conditions for process survival or extinction.
Martingale techniques applied to fragmentation with killing.
Abstract
We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth 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.
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Taxonomy
TopicsHeavy metals in environment · Coagulation and Flocculation Studies · Stochastic processes and statistical mechanics