Asymptotic moments of spatial branching processes
| hal.structure.identifier | Department of Mathematical Sciences [Bath] | |
| dc.contributor.author | GONZALEZ, Isaac | |
| hal.structure.identifier | Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL] | |
| dc.contributor.author | HORTON, Emma | |
| hal.structure.identifier | Department of Mathematical Sciences [Bath] | |
| dc.contributor.author | KYPRIANOU, Andreas | |
| dc.date.accessioned | 2024-04-04T02:43:17Z | |
| dc.date.available | 2024-04-04T02:43:17Z | |
| dc.date.issued | 2022-04-25 | |
| dc.identifier.issn | 0178-8051 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191319 | |
| dc.description.abstractEn | Suppose that X = (X t , t ≥ 0) is either a superprocess or a branching Markov process on a general space E, with non-local branching mechanism and probabilities P δx , when issued from a unit mass at x ∈ E. For a general setting in which the first moment semigroup of X displays a Perron-Frobenius type behaviour, we show that, for k ≥ 2 and any positive bounded measurable function f on E, lim t→∞ g(t)E δx [ f, X t k ] = C k (x, f) where the constant C k (x, f) can be identified in terms of the principal right eigenfunction and left eigen-measure and g(t) is an appropriate determinisitic normalisation, which can be identified explicitly as either polynomial in t or exponential in t, depending on whether X is a critical, supercritical or subcritical process.The method we employ is extremely robust and we are able to extract similarly precise results that additionally give us the moment growth with time of \int_0^t ⟨g, X_t⟩ds, for bounded measurable g on E. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Asymptotic behaviour | |
| dc.subject.en | Non-local branching | |
| dc.subject.en | Superprocesses | |
| dc.subject.en | Branching processes | |
| dc.subject.en | Moments | |
| dc.title.en | Asymptotic moments of spatial branching processes | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00440-022-01131-2 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| bordeaux.journal | Probability Theory and Related Fields | |
| bordeaux.page | 805-858 | |
| bordeaux.volume | 184 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03321803 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03321803v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Probability%20Theory%20and%20Related%20Fields&rft.date=2022-04-25&rft.volume=184&rft.spage=805-858&rft.epage=805-858&rft.eissn=0178-8051&rft.issn=0178-8051&rft.au=GONZALEZ,%20Isaac&HORTON,%20Emma&KYPRIANOU,%20Andreas&rft.genre=article |
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