Artículo
On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
Fecha de publicación:
02/2019
Editorial:
Institute of Mathematical Statistics
Revista:
Annales de L'institut Henri Poincare-probabilites Et Statistiques
ISSN:
0246-0203
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We give necessary and sufficient conditions for laws of large numbers to hold in L2 for the empirical measure of a large class of branching Markov processes, including λ-positive systems but also some λ-transient ones, such as the branching Brownian motion with drift and absorption at 0. This is a significant improvement over previous results on this matter, which had only dealt so far with λ-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is always strictly positive on the event of survival, and use this characterization to derive a simple method for simulating (quasi-)stationary distributions.
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Articulos (IC)
Articulos de INSTITUTO DE CALCULO
Articulos de INSTITUTO DE CALCULO
Citación
Jonckheere, Matthieu Thimothy Samson; Saglietti, Santiago; On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 56; 1; 2-2019; 265-295
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