Asymptotics of self-similar growth-fragmentation processes
| Autor: | Benjamin Dadoun |
|---|---|
| Přispěvatelé: | University of Zurich, Dadoun, Benjamin |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Uniform integrability Pure mathematics Self-similarity 01 natural sciences 010104 statistics & probability 510 Mathematics Mathematics::Probability 60J25 Convergence (routing) FOS: Mathematics Limit (mathematics) 1804 Statistics Probability and Uncertainty 0101 mathematics 2613 Statistics and Probability growth-fragmentation Mathematics self-similarity 010102 general mathematics Probability (math.PR) Statistics Probability and statistics Random walk Connection (mathematics) 10123 Institute of Mathematics 60G18 Probability and Uncertainty 60F15 Statistics Probability and Uncertainty Martingale (probability theory) Mathematics - Probability additive martingale |
| Zdroj: | Electron. J. Probab. |
| Popis: | Markovian growth-fragmentation processes introduced by Bertoin extend the pure fragmentation model by allowing the fragments to grow larger or smaller between dislocation events. What becomes of the known asymptotic behaviors of self-similar pure fragmentations when growth is added to the fragments is a natural question that we investigate in this paper. Our results involve the terminal value of some additive martingales whose uniform integrability is an essential requirement. Dwelling first on the homogeneous case, we exploit the connection with branching random walks and in particular the martingale convergence of Biggins to derive precise asymptotic estimates. The self-similar case is treated in a second part; under the so called Malthusian hypotheses and with the help of several martingale-flavored features recently developed by Bertoin et al., we obtain limit theorems for empirical measures of the fragments. 33 pages; published in EJP |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|