Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses

DOI10.1214/aop/1022855868zbMath0945.60090OpenAlexW1575670275MaRDI QIDQ1307449

Yves Le Jan, Jean-François Le Gall

Publication date: 12 October 2000

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022855868

zbMATH Keywords

moment functionalsgeneral branching mechanismLévy snakesuperprocessesoccupation field

Mathematics Subject Classification ID

Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Zooming in at the root of the stable tree, Feller property and infinitesimal generator of the exploration process, Growth of Lévy trees, Fragmentation at height associated with Lévy processes, The Gorin-Shkolnikov identity and its random tree generalization, A limit theorem for the contour process of conditioned Galton-Watson trees, A continuum-tree-valued Markov process, Path-valued branching processes and nonlocal branching superprocesses, Random real trees, A tree-valued Markov process associated with an admissible family of branching mechanisms, Fractional generalization of Kac integral, Smaller population size at the MRCA time for stationary branching processes, Fragmentation associated with Lévy processes using snake, Limit Theorems for Continuous-Time Branching Flows, Probabilistic and fractal aspects of Lévy trees, Skeletal stochastic differential equations for continuous-state branching processes, Williams' decomposition of the Lévy continuum random tree and simultaneous extinction probability for populations with neutral mutations, Random self-similar trees: a mathematical theory of Horton laws, Global regime for general additive functionals of conditioned Bienaymé-Galton-Watson trees, Branching processes in Lévy processes: The exploration process, Branching particle systems in spectrally one-sided Lévy processes

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