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Title: Subcritical multitype Markov branching processes with immigration generated by Poisson random measures Authors:  Maroussia Slavtchova-Bojkova - Sofia University (Bulgaria) [presenting]
Ollivier Hyrien - Fred Hutchinson Cancer Research Center (United States)
Nikolay Yanev - Bulgarian Academy of Sciences (Bulgaria)
Abstract: Multitype subcritical Markov branching processes with immigration driven by Poisson random measures are investigated. Limiting distributions are established for various rates of the Poisson measures when they are asymptotically equivalent to exponential or regularly varying functions. Results analogous to a strong LLN are proved, and limiting normal distributions are obtained when the local intensity of the Poisson measure increases with time. When it decreases, conditional limiting distributions are established. A stationary limiting distribution is obtained when the growth rate of the Poisson mean measure is asymptotically linear. The asymptotic behavior of the first and second moments of the processes is investigated as well.