【摘 要】
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Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state
【机 构】
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MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged,Szeged H-67
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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.
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