Almost sure, L1-and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration  被引量:1

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作  者:Mátyás Barczy Sandra Palau Gyula Pap 

机构地区:[1]MTA-SZTE Analysis and Stochastics Research Group,Bolyai Institute,University of Szeged,Szeged H-6720,Hungary [2]Department of Statistics and Probability,Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas,Universidad Nacional Autònoma de México,Ciudad de México 04510,México [3]Bolyai Institute,University of Szeged,Szeged H-6720,Hungary

出  处:《Science China Mathematics》2020年第10期2089-2116,共28页中国科学:数学(英文版)

基  金:supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciencessupported by the Royal Society Newton International Fellowship and the EU-funded Hungarian(Grant No.EFOP-3.6.1-16-2016-00008)。

摘  要:Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration(CBI process)converges almost surely.If an x log(x)moment condition on the branching mechanism does not hold,then the limit is zero.If this x log(x)moment condition holds,then we prove L1 convergence as well.The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing.If,in addition,a suitable extra power moment condition on the branching mechanism holds,then we provide the correct scaling for the projection of a CBI process on certain left non-Perron eigenvectors of the branching mean matrix in order to have almost sure and L1 limit.Moreover,under a second order moment condition on the branching and immigration mechanisms,we prove L2 convergence of an appropriately scaled process and the above-mentioned projections as well.A representation of the limits is also provided under the same moment conditions.

关 键 词:multi-type continuous state and continuous time branching processes with immigration almost sure L1-and L2-growth behaviour 

分 类 号:O211.63[理学—概率论与数理统计]

 

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