On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
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 s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/147402 |
| Acceso en línea: | http://hdl.handle.net/11336/147402 |
| Access Level: | acceso abierto |
| Palabra clave: | BRANCHING MARKOV PROCESSES H-TRANSFORM LAW OF LARGE NUMBERS SPINE DECOMPOSITION Λ-POSITIVITY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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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