期刊
ADVANCES IN APPLIED PROBABILITY
卷 53, 期 4, 页码 1023-1060出版社
APPLIED PROBABILITY TRUST
DOI: 10.1017/apr.2021.7
关键词
Multi-type continuous-state and continuous-time branching processes with immigration; mixed normal distribution
资金
- Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences
- Royal Society Newton International Fellowship
- EU [EFOP-3.6.1-16-2016-00008]
Under certain moment conditions on the branching and immigration mechanisms, this study demonstrates the asymptotic mixed normality of a scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on specific left non-Perron eigenvectors of the branching mean matrix. Additionally, asymptotic normality is proven under some conditional probability measure, along with the convergence of relative frequencies of distinct types of individuals on a suitable event.
Under a fourth-order moment condition on the branching and a second-order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In the case of a non-trivial process, under a first-order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.
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