2016/09/12 by Yan-Xia Ren, Renming Song, Ren, Yan-Xia +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1609.03265
openalex publication_date 2016/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We decompose the genealogy of a general superprocess with spatially dependent branching mechanism with respect to the last individual alive (Williams decomposition). This is a generalization of the main result of Delmas and Hénard [Electron. J. Probab.,18,1-43,2013] where only superprocesses with spatially dependent quadratic branching mechanism were considered. As an application of the Williams decomposition, we prove that, for some superprocesses, the normalized total mass will converge to a point mass at its extinction time. This generalizes a result of Tribe [Ann. Probab.,20,286-311,1992] in the sense that our branching mechanism is more general.