Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes
Idioma
en
Article de revue
Este ítem está publicado en
ALEA : Latin American Journal of Probability and Mathematical Statistics. 2022
Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....]
Fecha de defensa
2022Resumen en inglés
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth ...Leer más >
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term <i>stochastic</i> behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article, we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.< Leer menos
Palabras clave en inglés
Growth-fragmentation
Law of large numbers
Asynchronous exponential growth
Cell division
Ergodic theorem
Spectral radius
Spectral gap
Intrinsic martingale
Spectrally negative Lévy process
Dividend process
Skeleton decomposition
Orígen
Importado de HalCentros de investigación